Question

please solve it as soon as possible
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Answer 1

Rewrite :

(7²¹ + 7²² + 7²³ + 7²⁴)

7²¹ + 7²² + 7²³ + 7²⁴ = 7²¹ + 7²¹⁺¹ + 7²¹⁺² + 7²¹⁺³

= 7²¹.1 + 7²¹.7¹ + 7²¹.7² + 7²¹.7³

= 7²¹( 1 + 7 + 49 + 343 )

7²¹ × 400 / 25

→400 is divisible by zero,hence remainder is zero.

Answer 2

ANSWER

NOW....

$\frac{7 {}^{21} + 7 {}^{22} + 7 {}^{23} + 7 {}^{24} }{25} \\ = \frac{7 {}^{21}(1 + 7 {}^{1} + 7 {}^{2} + 7 {}^{3} ) }{25} \\ = \frac{7 {}^{21} (1 + 7 + 49 +34 3)}{25} \\ = \frac{7 {}^{21} \times 400}{25} \\ = 7 {}^{21} \times \frac{400}{25} \\ = 7 {}^{21} \times 16 \\ therefore \: there \: wont \: be \: any \: remainder \\ \: answer \: \: remainder = 0$