- #1
shizukusan
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Homework Statement
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)
Homework 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)
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.