My numbers
Number Theory
Level
pending
I choose two numbers:
- Both are positive integers..
- Their difference is a prime.
- Their product is a perfect square.
- Their sum's last digit is 3.
Then the sum of the squares of the two number is
The answer is 97.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
From 4. The numbers must be an even and an odd.
So to fit 3. The numbers themselves must be perfect squares.
All even perfect squares end in 0, 4, or 6.
All odd perfect squares end in 1, 5, or 9.
The only combination whose sum ends in 3 is 4+9.
Since the squares end in 4 and 9, their difference must end in 5.
The only prime that ends in 5 is 5 itself.
The only squares that are 5 apart are 4 and 9.
Hence, the two numbers are 4 and 9.
So the sum of their squares is = 16 + 81 = 97