Question

show that (15)ncan never end with digits zero for any natural number n
${15}^{n}$
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Answer 1

Answer:

For a number to end with zero, it should be a multiple of 10, i.e., it should be divisible by both 2 and 5. However, $15^{n}$ = $3^{n}$ × $5^{n}$. This means that the given number is divisible by 5, but is not divisible by 2. Thus, the number is not a multiple of 10. Hence, the proposition.