Find the smallest positive integer solution to

.

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- Mar 26th 2008, 09:30 AMperashFind the smallest positive
Find the smallest positive integer solution to

. - Mar 26th 2008, 10:16 AMJaneBennet

So find the smallest positive integer*x*such that . The answer should be . (I worked it out using Excel. (Tongueout)) - Mar 26th 2008, 05:32 PMThePerfectHacker
Here is a non-excel solution. First .

Thus, this is equivalent to,

Which gets simplified to,

The first and third congruences combine since .

In first congruence subtract 20 once, in second congruence subtract 9 three times. To get*,

Thus, .

*)You can use Chinese Remainder Theorem here, but I do not like to use that theorem, it is too computational. What you see here is my approach to combining modolus.