Question
If n is a positive integer, prove that $3^{3\text{n}}-26\text{n}-1$ is divisible by 676.
If n is a positive integer, prove that $3^{3\text{n}}-26\text{n}-1$ is divisible by 676.
$3^{3\text{n}}-26\text{n}-1$
$=(3^3)^\text{n}-26\text{n}-1$
$=27^\text{n}-26\text{n}-1$
$=(1+26)^\text{n}-26\text{n}-1$
$\Big({^\text{n}\text{C}}_0+{^\text{n}\text{C}}_1(26)^1+{^\text{n}\text{C}}_2(26)^2+.....+676(26)^{\text{n}-2}\Big)-26\text{n}-1$
$=676\Big({^\text{n}\text{C}}_2+......+(26)^{\text{n}-2}\Big)$
$\therefore3^{3\text{n}}-26\text{n}-1$ is divisible for $\text{n}\in\text{N}.$
Hence, proved
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Foci
$(\pm3, 0),$ a = 4| Marks | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| Frequency | 1 | 6 | 6 | 8 | 8 | 2 | 2 | 3 | 0 | 2 | 1 | 0 | 0 | 0 | 1 |
| Hights in inches | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 66 |
| No. of students | 15 | 20 | 32 | 35 | 35 | 22 | 20 | 10 | 8 |