Aptitude - Numbers - Discussion

Discussion Forum : Numbers - General Questions (Q.No. 3)

Numbers

It is being given that (2³² + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?

(2¹⁶ + 1)

(2¹⁶ - 1)

(7 x 2²³)

(2⁹⁶ + 1)

Answer: Option

Explanation:

Let 2³² = x. Then, (2³² + 1) = (x + 1).

Let (x + 1) be completely divisible by the natural number N. Then,

(2⁹⁶ + 1) = [(2³²)³ + 1] = (x³ + 1) = (x + 1)(x² - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.

Discussion:

137 comments Page 7 of 14.

Saurabh gupta said: 10 years ago

Dear sir I can't understand your explanation. Please explain clearly from basics.

Yuvraj said: 8 years ago

I can't understand to which way solve this question please explain in simple way.

Manoj said: 10 years ago

I can understand the problem. But is there any simplest method to solve this?

Manoj said: 10 years ago

I can understand the problem. But is there any simplest method to solve this?

Mohsin said: 1 decade ago

Ohh Its confusing !!!!!
I cant understand y take (2^96+1)??????????????????

Senthil kumar said: 1 decade ago

I cannot understand how this (2^23)^3+1 is created.

Please explain sir.

Karna said: 8 years ago

Here, We know that (x^n+y^n) is divisible by (x+a) for natural numbers.

Dibya said: 1 decade ago

Why it will not be divisible by 2^16+1?

As if 2^32 then why not 2^16?

Sravanthi said: 9 years ago

I don't understand this problem. Please explain it in a simple way.

Chethanya said: 1 decade ago

Please explain in simple method, because I'm from arts background.

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