n=617284
Find two integers whose squares have a difference of 1,234,567.
can you find two integers whose squares will produce a difference of any whole number you chose?
if so, how? if not, what kind of numbers can't be chosen.
well... a^2-b^2=1234567
we know a must end in a 1 or 9 and b must end in a 2 or 8 (this is to produce the seven at the end)
i came up with 617289^2-617288^2=1234577 and that's as close as i can get.
any suggestions? first time poster! sorry if it is an unusual / inappropriate post!
much thanks!
Hello, perfect square!
Galactus used a very clever bit of trivia.Find two integers whose squares have a difference of 1,234,567
Consecutive squares differ by consecutive odd numbers.
. .
. .
As he pointed out, we want two consecutive integers with a difference of 1234567.
So we have: .
. .
. . Hence: .
Therefore: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
I suspect that 1,234,567 is prime (but I'm not sure).
If the difference is a composite odd number,
. . there may be an alternate solution.
Example: Find two integers whose squares differ by 133.
Since , we have: .
. Since , we have: . .
. . . . . which can be written: . .
which are the differences of: .
Therefore: .