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$n$ | $n^2$ | $n+4$ | remainder |
---|---|---|---|
1 | 1 | 5 | 1 |
2 | 4 | 6 | 4 |
3 | 9 | 7 | 2 |
4 | 16 | 8 | 0 |
5 | 25 | 9 | 7 |
6 | 36 | 10 | 6 |
7 | 49 | 11 | 5 |
... | ... | ||
Not much pattern so far | |||
... | ... | ||
20 | 400 | 24 | 24$\times$15 = 240 + 120 = 360 24$\times$16 = 360 + 24 = 384 remainder is 16 |
100 | 10000 | 104 | 104$\times$100 = 10400 104$\times$96 = 10400 - 4016 = 10000 - 16 remainder is 16 |
101 | 10201 | 105 | 105$\times$100 = 10500 105$\times$97 = 10500 - 315 = 10200 - 16 remainder is 16 |
$n$ | $n+4$ | remainder when $16$ divided by $n+4$ |
---|---|---|
8 | 12 | 4 |
9 | 13 | 3 |
10 | 14 | 2 |
11 | 15 | 1 |
12 | 16 | 0 |