The Difference of Two Squares featuring

[@jesusborrego3270]

11:10 6!!!!!! Good video

[@YunruiHu]

Oh yes, another one with Blackpenredpen since the a level inequality video. I love you guys on youtube. always post interesting maths content. I subscribed

[@YunruiHu]

I don't if you know, but Tom Rock maths is also a fellow mathematician at oxford edit: he has a youtube channel too

[@JPiMaths]

@@YunruiHu thanks so much for the kind words! And glad you're enjoying both of our content! Yes, in fact I've had the pleasure of meeting Tom at Oxford!

[@stevenwilson5556]

I Immediately knew it was not possible, because perfect squares are always different by consecutive odd numbers, and to get an even difference between perfect squares you have to skip a middle square say 1 -> 4 -> 9, or adding two consecutive odd numbers, but 6 is the sum of 3 and 3, not consecutive odd numbers, so it cannot be the difference between two perfect squares.

[@stevenwilson5556]

For the part with = n. For starters, n can be any odd number, since consecutive perfect squares are different by an odd number. Next, n can be 0 if x = ± y. Then for even numbers besides 0 it is trickier. Any even number that is the sum of consecutive odd numbers would work, and even numbers that are the sum of the same odd number won't, so 2, 6, 10… So looks like anything that is congruent to 2 mod 4 is out, anything that is 0 mod 4 is fine, so every other even number works, starting with 0.

[@francaishaitam6708]

nice duo

[@JPiMaths]

Thank you very much! I've loved working with bprp!

[@Happy_Abe]

Not sure if there’s a closed form for general n but we would need that final square root term to be a perfect square and for the division by 2a to still be an integer if any such factor a of n

[@JPiMaths]

@@Happy_Abe yes that's true! Hats interesting is that we can also try other avenues. For example, we could consider cubes mod 9 and this immediately restricts certain values of n

[@Happy_Abe]

@@JPiMaths oh wow interesting, I’d be interested seeing more cases of this in a video!

[@SagarParajuli-r6c]

X2-Y2=6 does have a solution, (sqroot(6),0) satisfies it I dont get it

[@Jtak-qu5hk]

sqroot(6 is not an integer.)