### Theory NO. 1 : Number Theory

19Feb08

Prove that for every natural number there exists different natural numbers such as sum of any two is divisable by their diffrence.

Proof:

Because number is divisable by , we can write and of course . Adding those two together:

Induction:

1. Sequence 1,2 works

2. Assume that sequence works, then the number is divisable by the difference of any two numbers from the sequence

3. Let , then a sequence, including numbers:

‘Works’.

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Filed under: Mathematics, Theory | 1 Comment

Tags: math, natural, number theory, numbers

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I have a problem, how to you prove that 1 – 1 = 0 without using the above number theory, can you help me?