Discrete mathematics - Proper walk through of following proofs required ( for a better understanding )
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1) Prove that if n is an odd integer then n2 = 1 mod 8
2) Prove that 5n+3 is divisible by 4 for all intege ...
A proof and a solution involving a Diophantine equation - Show that the Diophantine equation x^2-y^2=n is solvable in integers if and only if n is odd or n is divisible by 4. When this equation is solvable, find all integer solutions.
Discrete mathematics proof - (See attached file for full problem description)
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Let d,m and n be positive integers with m>1 and m≡ 1 (mod d), let
n= c0+mc1+m2c2+m3c3+…+mrcr
be the base=m expansion of n, and le ...
Theory of Numbers - Euclid's Division Lemma - Theory of Numbers - Euclid's Division Lemma
(a) Prove that if a and b are odd integers , then a2 - b2 is divisible by 8.
(b) Prove that if a is an odd integer, then { a2 + (a + 2)2 + (a + 4 ...