Do Practice Through Solving These Questions !

Blazing goIITian

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13 Sep 2011 12:15:09 IST

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13 Sep 2011 12:15:09 IST

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Do Practice Through Solving These Questions !

AIEEE , IIT JEE

1.) Prove that there are infinitely many pairs (p,q) of primes such that p⁶ + q⁴ has two
positive divisors whose dierence is 4pq.

2.) Find all positive integers k and n such that kⁿ - 1 and n are divisible by precisely the
same primes.

3.) Determine all the primes that do not have a multiple in the sequence a_n = 2ⁿn² + 1,
n is greater than or eaual to 1.

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