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Originally Posted by ikhlas
n>0
the reminder when n is divided by 3 is 1 , and the reminder when n+1 is divided by 2 is 1 .
what is the reminder when n-1 is divided by 6
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This is a little tricky, takes more reasoning than math skills
it says the remainder when n is divided by 3 is 1
==> n = 3k + 1
and also the remainder when n + 1 is divided by 2 is 1
n + 1 = 2m + 1 ==> n = 2m ==> n is even number
but 3k + 1 then must be even ==> 3k must be odd
==> odd*odd = odd ==> k is odd
let k = 2j+1 ==> n = 3k + 1 = 3(2j + 1) + 1 = 6j + 4
==> n = 6j + 4, but we need n - 1 so we subtract 1 and...
==> n - 1 = 6j + 4 - 1 = 6j + 3 ==> the remainder when n - 1 is divided by 6 is 3