Congruence Classes: Solve the Hard Problem!

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SUMMARY

The discussion centers around the mathematical problem of congruence classes, specifically evaluating the expression (2^2^...^2)(n times) and its equivalence to (2^2^...^2)(n-1 times) mod n. The example provided illustrates that for n=2, the equation holds true as 4 is congruent to 2 modulo 2. Participants explore the implications of this congruence and its validity for other values of n, emphasizing the complexity of the problem.

PREREQUISITES
  • Understanding of modular arithmetic
  • Familiarity with exponentiation and its properties
  • Basic knowledge of congruence classes
  • Experience with mathematical proofs
NEXT STEPS
  • Research modular exponentiation techniques
  • Explore the properties of congruence relations
  • Study the implications of the Chinese Remainder Theorem
  • Investigate advanced topics in number theory related to exponentiation
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Mathematicians, students studying number theory, and anyone interested in advanced mathematical concepts related to congruence classes and modular arithmetic.

shaner-baner
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Here is a fun problem, it's hard to write out clearly, but I'll try to do it w/ little confusion.
Is it, or is it not true that
(2^2^...^2)(n times)=(2^2^...^2)(n-1 times) mod n
so for example, when [tex]n=2[/tex], [tex]2^2=2[/tex] ->
[tex]4=2[/tex] mod 2.
 
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He he sorry.
 
Last edited:

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