趣味的数学-192
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趣味的数学-192
a、b、c和d是正整数，有a^5 = b^4，c^3 = d^2，c - a = 19。
求 d - b。
趣味的数学-192
a、b、c和d是正整数，有a^5 = b^4，c^3 = d^2，c - a = 19。
求 d - b。
a = m^4
c = n^2
19 = c - a = (n + m^2)(n - m^2)
Since 19 is prime, n + m^2 = 19 and n - m^2 = 1.
n = 10 and m = 3
c = 100 and a = 81
d = 1000 and b = 243
d - b = 757