Suppose p and q are distinct primes such that ordp a = h and ordq a = k Prove that ordpq a= lcm(h, k) (just check the two conditions of order)

Q: Use the factorization A = PDP Ak= - 7 40 - 2 11 = 45 1 1 1 01 30 to compute A I -1 5 1 - 4 1 where k…

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Q: Suppose n ≥ 2 is an integer with the property that whenever a prime p divides n, p 2 also divides n…

A: let n=p1a1p2a2....pmam be the prime factorization of n  Here p1,p2....pm are all distinct primes and…

Q: 3. In this problem we use the notation for the digits a; of an integer m given by m = (akak-1...ao)…

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Q: Suppose p is an odd prime number, prove that p+1 (р — 3)! %3D (mod p) -

A: To prove: To prove that p-3!≡-p+12(mod p) for an odd prime number p.

Q: (g) 111... 111 (126 ones) (2) Prove that the numbers given in each part cannot be prime…

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Q: Show that there are no integers a, b such that a² + 2ab+26² = 100000000003. Hint. Use mod 4…

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Q: Suppose that a, b are two integers such that 3a? – b3 = 1. Does it follow that a and b are…

A: Given that a, b are two integers such that 3a2-b3=1.