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Binomial Theorem for Any Index

Find the rema...

Question

Find the remainder when $1565^{8} - 1551^{8}$ is divided by $14$ .

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Solution

$1565^{8} - 1551^{8} = (1565^{4} - 1551^{4}) (1565^{4} + 1551^{4}) = (1565^{2} - 1551^{2}) (1565^{2} + 1551^{2}) (1565^{4} + 1551^{4}) (1565 - 1551) (1565 + 1551) (1565^{2} + 1551^{2}) (1565^{4} + 1551^{4}) 14 \times (s o m e i n t e g e r) h e n c e g i v e n e x p r e s s i o n i s d i v i s i b l e b y 14, t h e r e f o r e r e m a i n d e r = 0$

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