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Question
If m, n are natural numbers, for what values of m, does 2n × 5m ends in 5?
Solution
2n × 5m
2n is always even for all values of n.
5m is always odd and ends with 5 for all values of m.
But 2n × 5m is always even and ends in 0.
∴ 2n × 5m cannot end with the digit 5 for any values of m.
No value of m will satisfy 2n × 5m ends in 5.
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