Math, asked by sanidhyasingla, 1 year ago

the number 107^90 - 76^90 is divisible by----> 61,62,64,none of these

Answers

Answered by siddhartharao77

= 107 - 76 = 31 and 107 + 76 = 183

So, 183 is divisible by 61.

So, The answer is 61.

sanidhyasingla: it is not any formula it is a2-b2 =(a-b)(a+b)

sanidhyasingla: there is no formula that you said

siddhartharao77: I am sorry. Its my fault.that is not a formula that is equation.

sanidhyasingla: please make me understand this question again and by full explanation

siddhartharao77: Since the power is same and both are even.
It’ll always be divisible by (a-b) and (a+b).

sanidhyasingla: i am unable to understand you

siddhartharao77: U said that u know this formula a^n-b^n. What does this formula mean?

siddhartharao77: I am just asking you that's it.

sanidhyasingla: please please make me understand

siddhartharao77: when n is even, a^n − b^n can be factored either with (a − b) as a factor or (a + b). In the given example 90 is even so it can be factored either with (a-b)(a+b).

Answered by throwdolbeau

Answer:

$\bf 107^{90}-76^{90}\textbf{ is divisible by 61}$

Step-by-step explanation:

$107^{90}\text{ is odd and }76^{90}\text{ is even}\\\\\text{So, their difference is odd hence cannot be divisible by 62 and 64}\\\text{Now, to check whether it is divisible by 61 or not}\\\text{Took the powers of 107 and 76 modulo 61}\\\\107^1\equiv 46\\\\107^2\equiv 46^2\equiv 2116\equiv 42\\\\76^1\equiv 15\\\\76^2\equiv 15^2\equiv 225\equiv 42$

So, 107² - 76² ≡ 0 modulo 61

Now, 107² - 76² is divisible by 61

$107^{90}-76^{90}=(107^2-76^2)(107^{88}+107^{86}\cdot 76^2+107^{84}\cdot 76^{4}......76^{88})\\\\\textbf{Hence, }\bf 107^{90}-76^{90}\textbf{ is divisible by 61}$

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