Square sums

hitler didi

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Sep 19, 2012
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62+72+=(the answer and the missing number should be in square)

x2++=
(the answer and the missing number should be in square)

and guys if u have any website regarding these type of sum plz post the link
 
62+72+=(the answer and the missing number should be in square)

x2++=
(the answer and the missing number should be in square)

and guys if u have any website regarding these type of sum plz post the link

Only way to do this (that I know of) is through programming or brute-force (spreadsheet)

62 + 72 = 85

Then check diffrence from 102, 112, 122, etc. and find when the differnce is a perfect square. (fixed my mistake ... those were supposed to be "to the power 2" )

We are lucky ... second number is a hit!!
 
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Only way to do this (that I know of) is through programming or brute-force (spreadsheet)

62 + 72 = 85

Then check diffrence from 102, 112, 122, etc. and find when the differnce is a perfect square.

We are lucky ... second number is a hit!!



i did not get it is there any other way of doing his sum:?:
 
62 + 72 + 62 = 112

62 + 72 + 422 = 432

Can I get out of corner now???!!
 
NO.
Btw, I still don't understand what's going on here...
Can someone reword the problem...like, what's "in a square" ?
What's purpose of "??" ?

My interpretation of the question was (like a 3D Pythagorean Theorem)

62 + 72 + M2 = N2

where M & N are integers.

I don't know what does "??" mean - but -

??? means :mad::mad::mad:
 
Last edited by a moderator:
62+72+=(the answer and the missing number should be in square)

x2++=
(the answer and the missing number should be in square)

and guys if u have any website regarding these type of sum plz post the link


If I understand you correctly, you are seeking solutions to x^2 + y^2 + z^2 = d^2.

How many rectangular solids can you define where all the edges and the internal diagonal are all integers?

Here, we have to satisfy the expression X^2 + Y^2 + Z^2 = d^2 where d = the internal diagonal. These can be derived from the expressions:
........X = p^2 + q^2 - r^2
.......Y = 2pr
.......Z = 2qr
.......d = p^2 + q^2 + r^2
One immediately obvious solution is 1^2 + 2^2 + 2^2 = 3^2. Some others are
X.....Y.....Z.......d

2.....3.....6.......7

1.....4.....8......9

3....16...24...29


How many rectangular solids can you define where all the edges, all the surface diagonals, and the internal diagonal are all integers?


To find such a box the expressions from above give rise to Y^2 + b^2 = d^2 or d^2 = [8mn(m^4 - n^4)]^2 + [(m^2 + n^2)^3]^2. A computer program can no doubt be created that will search for the smallest integer value of d, given one exists. I have found no solutions to date and do not, in fact, know if any exist.

Up to you Denis.
 
Aye, Aye, Tchr!

Keeping it to x < y < z < 100, there are 736 cases;
First 2: 1,4,8 : 9 and 1,6,18 : 19
Last 2: 80,90,96 : 154 and 86,91,98 : 159

Fantastic Denis. I knew you would come through.
 
In reply to PM from HitlerDiDi

62 + 72 + 62 = 112

62 + 72 + 422 = 432

I got these by brute-force (using excel) and using

62 + 72 + M2 = N2

where M & N are integers.

I started with N =10 and continued
 
Keeping it to x < y < z < 100, there are 736 cases;
First 2: 1,4,8 : 9 and 1,6,18 : 19
Last 2: 80,90,96 : 154 and 86,91,98

I knew you could do it Denis.

Thanks
 
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