1, 2, 3, 4, …

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a = bn (n ∈ ℤ)

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a = bn + m (m, n ∈ ℤ) (m < n)
25 = 8 * 3 + 1
19 = 4 * 4 + 3
108 = 21 * 5 + 3

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a = bn + m (n ∈ ℤ) (m ∈ W) (m < n)
n = 13
m < n, m ∈ W
m ∈ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

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0 = n·0 (n ∈ ℤ) 
n·0 = 0

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a = 3n (n ∈ ℤ)
a² = (3n)²
a² = 9n²

Պատ․ այո

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a = 5n + 4 (n ∈ ℤ)
a² = (5n + 4)²
a² = 25n² + 40n + 16
(25n² + 40n + 16)/5 = 5n² + 8n + 3 (1 մնացորդ)

Պատ․ 1

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a = 7n + 2 (n ∈ ℤ)
a³ + 5a = (7n + 2)³ + 5(7n + 2) = 
= 343n³ + 294n² + 84n + 8 + 35n + 10 = 
= 343n³ + 294n² + 119n + 18 

(343n³ + 294n² + 119n + 18)/7 = 49n³ + 42n² + 17n + 2 (4 մնացորդ)

Պատ․ 4 մնացորդ

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