show that any number of form 75ⁿ, n€N can never end with the digit 0?
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if 4n ends with 0 then it must have 5 as a factor. But we know the only prime factor of 4n is 2. Also we know from the fundamental theorem of arithmetic that prime factorization of each number is unique. Hence 4n can never end with the digit 0.
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refer the above picture
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