+1833 Find the last three digits of $5^{619}$. (Compute the remainder when $5^{619}$ is divided by 1000.)
+33615 The last three digits of 5n, when n>2, alternate between 125 (when n is odd) and 625 (when n is even).
Because 619 is odd the last three digits of 5619 are 125.
That means 5619/1000 = m + 0.125 where m is an integer, so 5619 = 1000m + 125
i.e. The remainder on dividing 5619 by 1000 is 125.
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+33615 The last three digits of 5n, when n>2, alternate between 125 (when n is odd) and 625 (when n is even).
Because 619 is odd the last three digits of 5619 are 125.
That means 5619/1000 = m + 0.125 where m is an integer, so 5619 = 1000m + 125
i.e. The remainder on dividing 5619 by 1000 is 125.
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