JEE MAIN - Mathematics (2021 - 17th March Morning Shift - No. 15)
If (2021)3762 is divided by 17, then the remainder is __________.
Odpowiedź
4
Wyjaśnienie
2021 = 17m - 2
(2021)3762 = (17m $$-$$ 2)3762 = multiple of 17 + 23762
= 17$$\lambda$$ + 22 (24)940
= 17$$\lambda$$ + 4 (17 $$-$$ 1)940
= 17$$\lambda$$ + 4 (17$$\mu$$ + 1)
= 17k + 4; (k $$\in$$ I)
$$ \therefore $$ Remainder = 4
(2021)3762 = (17m $$-$$ 2)3762 = multiple of 17 + 23762
= 17$$\lambda$$ + 22 (24)940
= 17$$\lambda$$ + 4 (17 $$-$$ 1)940
= 17$$\lambda$$ + 4 (17$$\mu$$ + 1)
= 17k + 4; (k $$\in$$ I)
$$ \therefore $$ Remainder = 4