Find the remainder when 7[50k-1] is divided by 50

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Solution

7[50k - 1] = 7[50k - 1 - 49] + 7 $\times$ 49 (we add and subtract 7 * 49)

= 7[50k - 50] + 300 + 43

The first two terms are multiple of 50

$\Rightarrow$ The remainder will be 43

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