Question: Let a,b be distinct prime numbers. Show that (a^(b-1) + b^(a-1) - 1) / (a*b) is an integer. Should be easy but Im just completly blanked out... Thank you
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Originally Posted by Fulger85 Question: Let a,b be distinct prime numbers. Show that (a^(b-1) + b^(a-1) - 1) / (a*b) is an integer. Should be easy but Im just completly blanked out... Thank you Hi Fulger85. By Fermat’s little theorem, divides therefore divides Similarly divides and so divides Hence divides
Understood. Thank you
Actually, do you mind elaborating on why lcm(a,b) divides it? Thanks
Originally Posted by Fulger85 Actually, do you mind elaborating on why lcm(a,b) divides it? Thanks Property of lcm. If then , for . --- Your problem can be generalized to for relatively prime positive integers .
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