Question

what is the remainder when 2^72 is divided by 1025
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Answer 1

Answer:

4722366482869645213696

1025

≈4.607186813⋅10¹8

hope it helps.

Answer 2

The remainder when 2^72 is divided by 1025 is 1021

Explanation:

We know that

$2^{10}=1024$

Thus,

$2^{72}=2^{70}\times 2^2$

$\implies 2^{72}=(2^{10})^7\times 2^2$

$\implies 2^{72}=(1024)^7\times 2^2$

Now

$1024^7$

$=(1025-1)^7$

$=^7C_0(1025)-^7C_1(1025)^6+^7C_2(1025)^5-^7C_3(1025)^4+^7C_4(1025)^3-^7C_5(1025)^2+^7C_6(1025)-^7C_7$

Thus,

$2^{72}=4(^7C_0(1025)-^7C_1(1025)^6+^7C_2(1025)^5-^7C_3(1025)^4+^7C_4(1025)^3-^7C_5(1025)^2+^7C_6(1025)-^7C_7)$

$4(^7C_0(1025)-^7C_1(1025)^6+^7C_2(1025)^5-^7C_3(1025)^4+^7C_4(1025)^3-^7C_5(1025)^2)+28(1025)-4$

Therefore if we subtract 4 from $2^{72}$, it will be completely divisible

In other way, the remainder on dividing $2^{72}$ by 1025 will be

$-4+1025=1021$

Hope this answer is helpful.

Know More:

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