proof or given a counter−example if p is prime and a∈N then p∣(a+p)^p −a^p


Question and Answers Forum

All Questions Topic List
Number Theory Questions
Previous in All Question Next in All Question
Previous in Number Theory Next in Number Theory
Question Number 469 by 123456 last updated on 25/Jan/15

$p r o o f o r g i v e n a c o u n t e r - e x a m p l e$ $i f p i s p r i m e a n d a \in N t h e n$ $p ∣ {(a + p)}^{p} - a^{p}$
	Answered by prakash jain last updated on 10/Jan/15

	${(a + p)}^{p} = \underset{i = 0}{\sum^{p}}^{p} C_{i} a^{i} p^{p - i}$ ${(a + p)}^{p} - a^{p} = \underset{i = 0}{\sum^{p - 1}}^{p} C_{i} a^{i} p^{p - i}$ $All terms on the expansion in RHS$ $include p as a factor .$ $Hence p ∣ {(a + p)}^{p} - a^{p}$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum