Let m and n be positive integers. Show that 25m+3n is divisible by 83 if and only if so is 3m+7n.
Problem
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Tags: algebra
fractals
19.04.2013 21:23
Multiply the first number by 30, giving 750m+90n, then reduce mod 83, giving 3m+7n.
EDIT: sure
maplestory
20.04.2013 00:05
please stop labeling your outlines as solutions.
mrdriller
29.11.2020 08:52
Suppose that 83|25m+3n then 83|25m-80n then 83|5m-16n then 83|88m-16n then 83|11m-2n then 83|-72m-2n then 83|72m+2n then 83|36m+n then 83|36m+84n then 83|3m+7n \leftrightarrow then 83|3m+7n then 83|3m+83*9m+7n+83n then 83|750m+90m then 83|25m+3n.