(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find, with proof, the smallest positive integer n that satisfy all the congruences.

n = 1 (mod 2)

n = 2 (mod 3)

n = 3 (mod 4)

n = 4 (mod 5)

n = 5 (mod 6)

n = 6 (mod 7)

n = 7 (mod 8)

n = 8 (mod 9)

n = 9 (mod 10)

2. Relevant equations

Let a,b,m within Z with m > 0. Then, a = b mod m is m|a-b.

(not sure if relevant or not)

3. The attempt at a solution

I tried to figure out what some of the ristriction on n

(ie - has to be odd since n = 1 (mod 2))

but didn't get too far.

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# Homework Help: Congruences / modulo

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