Abstract
Abstract Five is Dr. Googol’s favorite number, and 5-fold symmetry is his favorite symmetry. Would you care for a barrage of mathematical trivia befitting only the most ardent mathophiles? ® Not only is 5 the hypotenuse of the smallest Pythagorean triangle, but it is also the smallest automorphic number. Let me explain. A Pythagorean triangle is a right-angled triangle with integral sides. For example, the smallest Pythagorean triangle has side lengths 3, 4, and 5. An automorphic number n, when multiplied by itself, leads to a product whose rightmost digits are n. Not counting the trivial case of the number 1, 5 and 6 are the smallest automorphic numbers because 5 × 5 = 25 and 6×6 = 36. Examining a larger number, the square of 25 is 625. Note that 25 appears as the final 2 digits of 625.
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