Whenever there is a number, there is a beauty (old wisdom)

What is the value of k k that satisfies this equation: 2 k 1 ( 2 k 1 ) = 137438691328 2^{k-1}(2^{k}-1) = 137438691328 ?

17 none of the above 19 20

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2 solutions

Gaurav Chahar
May 14, 2016

Just check the last 2 digits of the given number . this can be done by checking the last digits of the given 2 factors first one is odd but second is even and the last two digits of number are 28 this clearly says that the odd factor's last digit is 7 and even factor's last digit is 4 so 19 is the answer

I could have given more improved solution but my phone has some limitations

Gaurav Chahar - 5 years, 1 month ago

Nice work. Me too when I solve problems from my Samsung. The solution looks so primitive.

Hana Wehbi - 5 years, 1 month ago
Hana Wehbi
May 21, 2016

The easiest way to tackle this problem is to plug-in the value for k k in the equation. Since he gave me the values of k k and k k satisfies my equation. it means the right value of k k should give me both sides equal and in our case k k = 19 19 works. Also, this is the seventh perfect number, so if you were familiar with these numbers, you would also notice that k k = 19 19 [another trick that would be helpful]

We need to love maths, not do questions by any means. We must solve questions by the methods which agree with our logic and reason

Gaurav Chahar - 5 years ago

So boring words

Gaurav Chahar - 5 years ago

Boring words of mine not yours

Gaurav Chahar - 5 years ago

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