show that a^phi(b) + b^phi(a) is congruent to 1 (mod ab), if a and b are relatively prime positive integers

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- Jun 29th 2009, 01:20 PMsilentbobeulers theorem problem
show that a^phi(b) + b^phi(a) is congruent to 1 (mod ab), if a and b are relatively prime positive integers

- Jun 29th 2009, 01:40 PMBruno J.
__Hint__

Use Euler's theorem to show :

and conclude that . - Jun 29th 2009, 08:55 PMsilentbob
how can I prove that a^phi(b) + b^phi(a) is congruent to 1 (mod a (or b))?

- Jun 29th 2009, 09:13 PMo_O
Euler's theorem:

Clearly:

So: - Jun 30th 2009, 12:34 AMMoo
A more direct way : http://www.mathhelpforum.com/math-he...rithmetic.html