How many perfect square possible (1/2/3) in following numbers. 1) a^2 + b + c 2) b^2 + a + c 3) c^2 + a + b
Given that a,b,c are positive integers.
No solution possible since if a^2 = b+c and b^2 = a+c then their difference a^2 - b^2 = b - a is true but then since a^2 - b^2 = (a - b)(a + b) (dividing both sides by (a + b) yields a + b = -1 which cannot occur if all three numbers are positive integers
Find the sum of all the prime numbers larger than 2 less than 10^12 that are 1 more than a perfect square. Because the number can get pretty big provide the answer mod 1007.
Note: Problem shouldn't take much more than one minute if your answer is taking too long consider looking for optimizations.
If 1^3 + 2^3 + 3^3 = m^2 where m is also an integer. What are the next three consecutive positive integers such that the sum of their individual cubes is equal to a perfect square?
If a, b, and c are distinct numbers, how many solutions are there to the following equation?
