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min N = 5mod7, 8 mod6, 9 mod7

Source: 2020 New Zealand MO Round 2 p2 NZMO

September 22, 2021
number theoryremainder

Problem Statement

Find the smallest positive integer NN satisfying the following three properties. ∙\bullet N leaves a remainder of 55 when divided by 77. ∙\bullet N leaves a remainder of 66 when divided by 8 8. ∙\bullet N leaves a remainder of 77 when divided by 99.
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