Order of an Element in Math Olympiad Number Theory - EPISODE 1

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Learn about order of an element, its connection with group theory and number theory. We start with a motivating problem.

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Problem Source: Number Theory Structures, Examples, and Problems
Authors: Andreescu, Titu, Andrica, Dorin
  1. Cheenta Academy for Olympiad & Research
  2. Indian Statistical Institute
  3. Chennai Mathematical Institute
  4. Math Olympiad
  5. RMO
  6. IMO
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Автор

We essentially get from the fundamental theorem on orders that n | 2^2004
Then we see that n is of the form 2^k
Then we factor out 17^n-1 with difference of squares and calculate the 2 Adic valuation of each bracket.If one knows the LTE lemma then V2(17^n-1)=4+k seems direct.

yashvardhan
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Many institutes like unacadaemy and vedantu are giving free classes of PRMO on YouTube do you plan to start the same

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