オリジナル
distinct:明確(deepl翻訳より）
1-1. ユークリッドの互除法のやり方
Result
60
Prime factorizations
300 = 2^2×3×5^2 (5 prime factors, 3 distinct)
780 = 2^2×3×5×13 (5 prime factors, 4 distinct)
1-2. ユークリッドの互除法がなぜ必要か
Result
80
Prime factorizations
160 = 2^5×5 (6 prime factors, 2 distinct)
1200 = 2^4×3×5^2 (7 prime factors, 3 distinct)
計算ステップ回数が最悪になるケース
Result
1
Prime factorizations
89 is prime
144 = 2^4×3^2 (6 prime factors, 2 distinct)
3-2. 一次不定方程式 ax + by = c の整数解を求める具体例
Integer solution
x = 30 n + 12, y = -11 n - 4, n element Z
Result
x = -6 (5 n + 3) and y = 11 n + 7 and n element Z
Examples of integer solutions
y = 18 and x = -48
(つづく)
3-4. 拡張ユークリッドの互除法のアルゴリズム的記述
Integer solution
x = 10 n + 3, y = -37 n - 11, n element Z
Result
x = -10 n - 7 and y = 37 n + 26 and n element Z
Examples of integer solutions
y = 63 and x = -17
(つづく)
参考