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The proof that a factorization into a product of powers of primes is unique up to the order of factors uses additional results on

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Use the division algorithm to find the quotient and the remainder when 76 is divided by 13

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Most theorems homework or test problems that you want to prove are either explicitly or implicity in the form If P Then Q In the

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Divisibility Proof Examples free interactive worked example from the Number Theory course on Axiom Academy Learn by doing

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The transitive property of divisibility states that if A B and A C then A is a common divisor of both B and C This isn t just a

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Proposition Let a b and c be integers If a b and b c then a c Note By assuming that a b then a 0 By

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For integers a 0 and b we will say that a divides b and write a b if there is an integer c such that b ac Also a is a factor of b

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Divisibility Theory free interactive lesson from the Intro to Proofs course on Axiom Academy Learn by doing with clear visual

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Result 4 1 let a b c Z with a 0 and b 0 If a b a b and b c b c then a c a c Proof Assume a b a b and b c b c Then b