❤️ Fast Powering Algorithm

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1
https://en.wikipedia.org/wiki/Exponentiation_by_squaring
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2
https://exploringnumbertheory.wordpress.com/tag/fast-powering-algorithm/
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3
http://homepages.math.uic.edu/~leon/cs-mcs401-s08/handouts/fastexp.pdf
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4
https://courses.cs.washington.edu/courses/cse311/21wi/resources/reference-modular-exponentiation.pdf
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5
https://www.rookieslab.com/posts/fast-power-algorithm-exponentiation-by-squaring-cpp-python-implementation
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6
https://www.johndcook.com/blog/2008/12/10/fast-exponentiation/
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7
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8
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9
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10
https://stackoverflow.com/questions/9434183/whats-the-fastest-algorithm-to-perform-exponentiation
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11
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12
https://planetcalc.com/8979/
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13
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14
https://www.programminglogic.com/fast-exponentiation-algorithms/
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15
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16
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17
https://leetcode.com/problems/powx-n/discuss/1869646/Illustration-of-Fast-Power-Algorithm-Exponentiation-by-Squaring-or-Binary-Exponentiation
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18
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19
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20
https://dev-notes.eu/2019/12/Fast-Modular-Exponentiation/
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21
http://www.math.clemson.edu/~sgao/papers/GGPS00.pdf
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22
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23
https://eli.thegreenplace.net/2009/03/21/efficient-integer-exponentiation-algorithms
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24
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25
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26
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27
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28
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29
https://link.springer.com/content/pdf/10.1007/s13369-017-2797-3.pdf
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30
https://www.scaler.com/topics/data-structures/binary-exponentiation/
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31
https://www.codespeedy.com/fast-exponentiation-python/
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32
https://courses.engr.illinois.edu/cs473/fa2010/Lectures/lecture7.pdf
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33
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34
https://primes.utm.edu/glossary/xpage/BinaryExponentiation.html
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35
https://crypto.stanford.edu/pbc/notes/numbertheory/exp.html
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36
https://www.quora.com/What-are-some-fast-algorithms-for-computing-the-nth-power-of-a-number
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37
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38
https://cryptography.fandom.com/wiki/Modular_exponentiation
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39
https://epubs.siam.org/doi/pdf/10.1137/1.9781611976496.14
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40
https://www.cs.cmu.edu/~cburch/survey/recurse/fastexp.html
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41
https://github.com/neeldani/Parallel-Matrix-Fast-Exponentiation-Algorithm
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42
https://arxiv.org/abs/1207.0511
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43
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44
https://allmathconsidered.wordpress.com/2015/07/10/a-fast-way-to-do-modular-exponentiation/
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45
https://www.algotree.org/algorithms/numeric/fast_exponentiation/
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46
https://www.bmoeller.de/pdf/expcache-eprint-2007-470.pdf
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47
https://empslocal.ex.ac.uk/people/staff/rjchapma/courses/nt13/binpow.pdf
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48
https://eprint.iacr.org/2011/239.pdf
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49
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50
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51
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52
https://www.sciencedirect.com/science/article/pii/S1877050920310565
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53
https://iq.opengenus.org/binary-exponentiation/
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54
https://www.semanticscholar.org/paper/An-Efficient-Modular-Exponentiation-Algorithm-Power-Sun-Huai/615f9c9bb7af80244aad22fdee28ff14fc663688
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55
https://dl.acm.org/doi/abs/10.1145/3439706.3447042
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56
https://www.hackerearth.com/practice/notes/matrix-exponentiation-1/
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57
https://www.ics.uci.edu/~irani/w17-6D/BoardNotes/07_RecursiveAlgorithmsPost.pdf
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58
https://cr.yp.to/papers/pippenger.pdf
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59
https://helloacm.com/exponentiation-by-squaring/
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60
https://www.cs.uaf.edu/2013/spring/cs463/lecture/02_13_multiplication.html
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61
https://www.numerade.com/ask/question/use-the-algorithm-for-fast-modular-exponentiation-to-compute-553-mod-9-18955/
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62
https://alvaro-videla.com/2014/03/the-power-algorithm.html
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63
https://www.baeldung.com/cs/integer-based-power-function
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64
https://www.researchgate.net/publication/320084242_Comparative_Study_of_Efficient_Modular_Exponentiation_Algorithms
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65
https://ijret.org/volumes/2015v04/i12/IJRET20150412049.pdf
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66
https://www.php.net/manual/en/function.bcpowmod.php
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67
https://asecuritysite.com/encryption/modarith
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68
https://www.tutorialspoint.com/cplusplus-program-to-implement-modular-exponentiation-algorithm
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69
https://medium.com/@tushargautamk21/fast-exponentiation-962e608e413e
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70
https://www.boxentriq.com/code-breaking/modular-exponentiation
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71
https://wiki.c2.com/?IntegerPowerAlgorithm
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72
https://afteracademy.com/blog/calculate-power-function
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73
https://scialert.net/abstract/?doi=tasr.2012.240.247
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74
https://www.academia.edu/49582100/Transitive_Closure_of_a_Graph_using_Graph_Powering_and_Further_Optimization_by_Eulers_Fast_Powering_Algorithm
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75
https://hal.archives-ouvertes.fr/hal-01185249/document
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76
https://sites.google.com/site/joshmaxwellcsis3000/home/week-03/ex07-write-a-biginteger-version-of-fast-modularexponentiation--test-it-with-5-different-cases-using-random-bigintegers-on-1024-bits-for-base-exponent-and-modulus--the-speedup-over-the-nave-algorithm-should-be-roughly-10300-to-1--explain-why
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77
https://www2.math.upenn.edu/~mlazar/math170/notes06-3.pdf
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78
https://www.sanfoundry.com/cpp-program-implement-modular-exponentiation-algorithm/
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79
https://mpark.github.io/programming/2014/08/18/exponentiation-by-squaring/
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80
https://kukuruku.co/post/automatic-algorithms-optimization-via-fast-matrix-exponentiation/
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81
https://mathoverflow.net/questions/13843/how-to-quickly-determine-whether-a-given-natural-number-is-a-power-of-another-na
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82
https://caslab.csl.yale.edu/publications/deshpande2021modular.pdf
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83
http://www.cs.toronto.edu/~denisp/csc373/docs/repeated_squaring_binary_search.pdf
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84
https://icpc.ninja/Algorithms/Bit/FastPower/
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85
https://javascript.plainenglish.io/javascript-algorithm-power-2cbedf59f40c
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86
http://math0.wvstateu.edu/~baker/cs405/code/Power.pdf
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87
https://slideplayer.com/slide/8262407/
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88
https://www.unite.ai/algorithm-predicts-processor-power-consumption-incredibly-fast/
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89
https://www.nayuki.io/page/fast-fibonacci-algorithms
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90
https://codecrucks.com/exponential-problem-solving-using-divide-and-conquer/
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91
https://www.hindawi.com/journals/jam/2014/107109/
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92
https://www.bryanblog.com/archives/1405
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93
https://brainly.com/question/14821885
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https://www.microsoft.com/en-us/research/wp-content/uploads/1996/01/j37acmon.pdf
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