モジュロ演算(剰余演算)
mod pのpが素数のときは割り算も定義される。素数でないとき、二つの数のかけ算にならない剰余があるため、割り算は定義できない。
mod2
0 + 0 = 0
0 + 1 = 1
1 + 1 = 0
0 × 0 = 0
0 × 1 = 0
1 × 1 = 1
mod3
0 + 0 = 0
0 + 1 = 1
0 + 2 = 2
1 + 1 = 2
1 + 2 = 0
2 + 2 = 1
0 × 0 = 0
0 × 1 = 0
0 × 2 = 0
1 × 1 = 1
1 × 2 = 2
2 × 2 = 1
mod5
0 + 0 = 0
0 + 1 = 1
0 + 2 = 2
0 + 3 = 3
0 + 4 = 4
1 + 1 = 2
1 + 2 = 3
1 + 3 = 4
1 + 4 = 0
2 + 2 = 4
2 + 3 = 0
2 + 4 = 1
3 + 3 = 1
3 + 4 = 2
4 + 4 = 3
0 × 0 = 0
0 × 1 = 0
0 × 2 = 0
0 × 3 = 0
0 × 4 = 0
1 × 1 = 1
1 × 2 = 2
1 × 3 = 3
1 × 4 = 4
2 × 2 = 4
2 × 3 = 1
2 × 4 = 3
3 × 3 = 4
3 × 4 = 2
4 × 4 = 1
加筆中…
整数(数学A)
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ピタゴラス数の例01947
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モジュロ演算(剰余演算)0715
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数と素数の性質0767