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I could just use division and modulus in a loop, but this is slow for really large integers. The number is stored in base two, and may be as large as 2^8192. I only need to know if it is a power of ten, so I figure there may be a shortcut (other than using a lookup table).
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Given two positive numbers x and y, check if y is a power of x or not. A simple solution is to repeatedly compute powers of x. If a power becomes equal to y, then y is a power, else not.
Any mathematical trick? First check if last digit is 5. If last digit is 5; divide it by 5. If result of division is 1, then number is power of 5.
If your number x is a power of ten then
x = 10^y
for some integer y, which means that
x = (2^y)(5^y)
So, shift the integer right until there are no more trailing zeroes (should be a very low cost operation) and count the number of digits shifted (call this k). Now check if the remaining number is 5^k. If it is, then your original number is a power of 10. Otherwise, it's not. Since 2 and 5 are both prime this will always work.
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