A powerful number is a positive integer such that every prime that appears in its prime factorization appears there at least twice. Erdős, Mollin and Walsh conjectured that three consecutive powerful numbers do not exist. This paper shows that if they do exist, the smallest of the three numbers must have remainder 7, 27, or 35 when divided by 36.

Author Bio

Edward Beckon is in 9th grade at Oliver Wendell Holmes Junior High in Davis, CA. He is taking a calculus class at Davis Senior High School.

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