Help me with this.

Find minimum 2 digit n, such that (7n+7n1+7n2+......+73+72+71+70)(7^{n} + 7^{n-1} + 7^{n-2} + ...... + 7^{3} + 7^{2} + 7^{1} + 7^{0}) is a perfect square, since known (73+72+71+70)(7^{3} + 7^{2} + 7^{1} + 7^{0}) is a perfect square.

Note : n3n \neq 3 !!!

Note by Bryan Lee Shi Yang
4 years, 8 months ago

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I am sorry, bcs. I have no answer.

Bryan Lee Shi Yang - 4 years, 8 months ago

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If you take n=0n=0, then you expression will be equal to 11 which is a perfect square. So n=0n=0 can be the one value. Also try to use the latex coding in your notes and problems (now I've put latex in it) , if you need a guide for latex, you can find it just by clicking here .!!! @Bryan Lee Shi Yang

Sandeep Bhardwaj - 4 years, 8 months ago

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Up till n=22, only n=0 and n=4 are perfect square according to what I get from TI -83+ calculator. After that I do not get accurate calculations.

Niranjan Khanderia - 4 years, 8 months ago

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There is no solution < 270.

D G - 4 years, 8 months ago

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Are there any solutions bigger than 270?

Bryan Lee Shi Yang - 4 years, 8 months ago

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CAN U WRITE A PROOF TO SUPPORT THIS

vishwesh agrawal - 4 years, 8 months ago

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n=37n = 37 satisfies!

Kartik Sharma - 4 years, 8 months ago

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>> n = 4

>> while (((7(n+1)-1)/6)0.5 - int(((7(n+1)-1)/6)0.5)) != 0:

                     n = n+1

My code! *Easy code, though!

Kartik Sharma - 4 years, 8 months ago

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No it doesn't. 21655801907853836686195357616408 is not a square number.

D G - 4 years, 8 months ago

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@D G 73816=21655801907853831608163177358336=46535794726053442\frac{{7}^{38}-1}{6} = 21655801907853831608163177358336 = {4653579472605344}^{2}

Kartik Sharma - 4 years, 8 months ago

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@Kartik Sharma http://www.wolframalpha.com/input/?i=%287%5E38+-+1%29%2F6+&dataset=

Siddhartha Srivastava - 4 years, 8 months ago

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@Siddhartha Srivastava There has to be a problem with my python idle, then. Thanks!

Kartik Sharma - 4 years, 8 months ago

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@Kartik Sharma Sorry, it is +1, not -1.

Bryan Lee Shi Yang - 4 years, 8 months ago

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@Bryan Lee Shi Yang Oh maybe. My IDLE is just reversing it up. When I replace - with +, it shows the above value(which should come with -).

Kartik Sharma - 4 years, 8 months ago

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