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Discrete mathematics proofs - 1) Prove that all integers a,b,p, with p>0 and q>0 that
((a+b) mod p)mod q = (a mod p) mod q + (b mod p) mod q
Or give a counterexample
2) prove for all integers a,b,p,q with p>0 and q>0 that
( ...
Discrete Math : Number of Solutions to Equations - a) Let n and r be positive integers. Explain why the number of solutions of the equation x1 + x2 + … + xn = r, where xi is a nonnegative integer for i = 1, 2, 3, …, n, equals the number of r-combinat ...
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 ...
Discrete mathematics questions - (See attached file for full problem description with proper symbols and equations)
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1)Prove that for any non-empty sets
A x (B-C) = (AxB)-(AxC)
2) Let a,b be integers and m a positive integ ...