Two primes whose squares have a difference of 42 are 7and 11.
72 = 2 x 2 x 2 x 3 x 3
They are different prime factors of a number, as opposed to repeated factors.For example, the prime factorisation of 12 is 2*2*3. The distinct primes of 12 are 2 and 3.
There are infinitely many such numbers.If p is a prime then p^11 has 12 factors.If p and q are any two primes, then p*q^5 has 12 factors.If p and q are any two primes, then p^2*q^3 has 12 factors.If p, q and r are any three primes, then p*q*r^2 has 12 factors.
The squares can have sides equal to each factor that is common to both numbers.
24 and 36
72 - 52 = 24 132 - 112 = 48 112 - 72 = 72
2 * 33 * 72
3136 = 26*72
As a product of its prime factors: 2*2*2*3*3 = 72
72 - 52 = 49 - 25 = 24
Let the numbers be 'n' & 'n+2' Hence their squares are n^(2) + (n+2)^(2) Their sum is n^(2) + (n+2)^(2) = 130 Multipoly out the second set of brackets n^(2) + n^(2) + 4n + 4 = 130 Collect like terms 2n^(2) + 4n - 126 = 0 Factor our '2' n^(2) + 2n - 63 = 0 It is now in quadratic form ; factor (n + 9)(n - 7) = 0 n = -9 & n = 7 Are the tweo odd numbers.
2 x 2 x 2 x 3 x 3 = 72
The Hollywood Squares - 1965 2-72 is rated/received certificates of: USA:TV-PG
72 plus 19 = 91
72 = 2 x 2 x 2 x 3 x 3
72
98 and 72