Multiples and primes

JEE Advanced 2015 Guidance › Olympiad Stuff questions › Multiples and primes

If m is a prime number,and a,b ,two numbers less than m prove that a^m-2+a^m-3b+a^m-4b²+...b^m-2 is a multiple of m

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akash93 ·2009-08-23 23:29:26

the sum comes out to be b^m-1-a^m-1b-a
since a and b are less than m and m is a prime
they are naturally coprime to it
b^m-1â‰¡1(modm)
a^m-1â‰¡1(modm)

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Basic Integral Calculus Operators Symbols Matrix Cases

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Multiples and primes

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