If (2021)3762 is divided by 17, then the remainder is __________.
Answer (integer)
4
Solution
2021 = 17m - 2
<br><br>(2021)<sup>3762</sup> = (17m $-$ 2)<sup>3762</sup> = multiple of 17 + 2<sup>3762</sup><br><br>= 17$\lambda$ + 2<sup>2</sup> (2<sup>4</sup>)<sup>940</sup><br><br>= 17$\lambda$ + 4 (17 $-$ 1)<sup>940</sup><br><br>= 17$\lambda$ + 4 (17$\mu$ + 1)<br><br>= 17k + 4; (k $\in$ I)<br><br>$\therefore$ Remainder = 4
About this question
Subject: Mathematics · Chapter: Binomial Theorem · Topic: Binomial Expansion
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