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Let alpha = log10 15 and beta = log10 16...

Let `alpha = log_10 15 and beta = log_10 16, a set A = {log_10 1, log_10 2,.....,log_10 50}` then find the number of elements in set A which can be written in the form of `aalpha + b beta + c=0` where a,b,c are in rational numbers.

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