Problem 142

sker · Post by **sker** » Sun May 31, 2009 11:32 pm

What am I supposed to submit in this problem? x + y + z? Because I think I have the right answer, as confirmed by two other sources, but the problem won't accept it.

Could someone please verify if my answer is right or wrong?

(Link to problem added by moderator: Problem 142 (View Problem))

daniel.is.fischer · Post by **daniel.is.fischer** » Sun May 31, 2009 11:40 pm

Yes, you should submit the sum.
You can PM me your answer and I'll check if it's correct.
You might also try resubmitting it, in case copy-pasting the answer added a space or lost a digit.

MaJJ · Post by **MaJJ** » Wed Aug 04, 2010 11:25 pm

What's wrong with (993250,949986,856350) = 2799586? My guess is that it's not the smallest solution, is it?

genious999 · Post by **genious999** » Thu Aug 05, 2010 1:00 am

Nope, it's not.

JMW1994 · Post by **JMW1994** » Sun Sep 25, 2011 4:49 am

In this problem, is a perfect square considered one that gives an integer when you square root x+y,x-y,y+z,y-z,x+z, and x-z?

rayfil · Post by **rayfil** » Sun Sep 25, 2011 4:59 am

JMW1994 wrote:In this problem, is a perfect square considered one that gives an integer when you square root x+y,x-y,y+z,y-z,x+z, and x-z?

Correct

Loers · Post by **Loers** » Sat Aug 25, 2012 7:48 am

How can I find integer solutions for this equation
a^2 + b^2 + c^2 - d^2 = 2e

is there some sort a tutorial or a specific part of math that handles this ?

thundre · Post by **thundre** » Mon Aug 27, 2012 5:06 pm

Loers wrote:How can I find integer solutions for this equation
a² + b² + c² - d² = 2e
is there some sort a tutorial or a specific part of math that handles this ?

That is called a "Diophantine equation".

BTW I edited your text to use the "sup" tag for superscripts. It's probably easier than generating an image.

Slaunger · Post by **Slaunger** » Sun Sep 29, 2013 8:35 pm

I have a solution to this problem with x + y + z = 1639329, which obey the conditions, but apparently not with the lowest possible sum. Obviously, I have missed some possibilities in my solution space

1. Can someone confirm that the sum 1639329 is in the spectrum of solutions, which comply with the conditions (just not the lowest sum) to check my understanding of the problem?

2. I can rapidly find plenty of other solutions with larger sums, the first four being
6557316
6645958
14610433
14753961
...
Could someone hint to me, what I kind of possibilities I appear to be missing in my spectrum of solutions? Perhaps pm me?

I have been stuck on this problem for almost two years now, and it is driving me nutz.

But I am very stubborn, and will not begin on a new problem until I have found a solution to this one...

Thanks

TheEvil · Post by **TheEvil** » Sun Sep 29, 2013 9:33 pm

The correct answer is lower than yours. It has the same number of digits as yours.
By the way: you can check any of your answers easily with a calculator, the hard part is to find the smallest one.

Slaunger · Post by **Slaunger** » Mon Sep 30, 2013 11:01 pm

TheEvil wrote:The correct answer is lower than yours. It has the same number of digits as yours.
By the way: you can check any of your answers easily with a calculator, the hard part is to find the smallest one.

Köszönjük!

I got encouraged by this, and recheked my assumptions. It turned out I had been too sloppy in assuming something about the ordering of the perfect squares, which was not entirely correct. Reran taking that into account and got the answer. Hurray. I am back in business on PE after almost two years!

Muahahahaaa.

Oliver1978 · Post by **Oliver1978** » Wed Feb 11, 2015 10:47 pm

Do you consider 1 a square? Actually, I don't, although 1 * 1 = 1.

dawghaus4 · Post by **dawghaus4** » Wed Feb 11, 2015 11:34 pm

leghorn wrote:Do you consider 1 a square? Actually, I don't, although 1 * 1 = 1.

Yes, 1 is a square number

Definition: A square number is an integer that is the square of an integer; that is, a number is square if it is the product of some integer with itself.

Since 1 = 1 * 1 and 1 is an integer, it satisfies the definition.

Also, if you wish, you can look at problem 61 where the first 5 squares are listed: 1, 4, 9, 16. 25...

One can go further and say that 1 is a prefect n^th power for all integers n ≥ 1.

The same can be said about 0. (Of course, in this problem, 0 is excluded because x > y > z > 0.)

Tom

Oliver1978 · Post by **Oliver1978** » Wed Feb 11, 2015 11:51 pm

Alrighty! Thanks for lighening this up.

RishadanPort · Post by **RishadanPort** » Mon Jul 29, 2019 1:05 am

Can x/y/z be negative? Question doesn't say they need to be positive

mdean · Post by **mdean** » Mon Jul 29, 2019 1:57 am

RishadanPort wrote: Mon Jul 29, 2019 1:05 am Can x/y/z be negative? Question doesn't say they need to be positive

The question mentions x > y > z > 0.

RishadanPort · Post by **RishadanPort** » Mon Jul 29, 2019 3:45 am

Ah oops missed that part. Thanks

mdean · Post by **mdean** » Fri Sep 06, 2024 5:33 pm

Hmm... My program appears to be calculating things correctly, but I seem to be missing a lot of solutions based on what's here. All the solutions I've found so far are with x, y, and z all even. I'm not sure how to troubleshoot it at this point except find a solution my program didn't find, then figure out why it didn't find it.

I could use some help from someone else on that. The only other recourse is to try to reverse engineer one of the values of x+y+z posted here and attempt to figure out x, y, and z.

Update: Nevermind. I'm an idiot. It took way too long to notice what was wrong.

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