ABC is three prime numbers and the product of ABC is five times of the sum of ABC. How much is the sum of a ^ 2 + B ^ 2 + C ^ 2 abc=5(a+b+c) Because a, B, C are all prime numbers, so one of a, B, C is 5, and because the band formula is rotational symmetry, any change of the order of a, B, C does not affect the result Let a = 5 To 5BC = 25 + 5B + 5C Divide both sides by 5 bc=5+b+c bc-b-c+1=6 (b-1)(c-1)=6=1*6=2*3 If it is decomposed into 2 * 3, then B and C are 3 and 4 respectively So (B-1) (C-1) = 1 * 6 Let B-1 = 1 and C-1 = 6 So B = 2, C = 7 a^2+b^2+c^2=5^2+2^2+7^2=78 Why does ABC have a number of 5

ABC is three prime numbers and the product of ABC is five times of the sum of ABC. How much is the sum of a ^ 2 + B ^ 2 + C ^ 2 abc=5(a+b+c) Because a, B, C are all prime numbers, so one of a, B, C is 5, and because the band formula is rotational symmetry, any change of the order of a, B, C does not affect the result Let a = 5 To 5BC = 25 + 5B + 5C Divide both sides by 5 bc=5+b+c bc-b-c+1=6 (b-1)(c-1)=6=1*6=2*3 If it is decomposed into 2 * 3, then B and C are 3 and 4 respectively So (B-1) (C-1) = 1 * 6 Let B-1 = 1 and C-1 = 6 So B = 2, C = 7 a^2+b^2+c^2=5^2+2^2+7^2=78 Why does ABC have a number of 5

abc=5(a+b+c)
Because 5 is a prime factor, that is, it can not be decomposed (if 5 is replaced by a composite number, for example, 6 = 2 * 3, then 2 can be included in a, 3 can be included in B, and the whole 6 can also be in a separate number of ABC. However, 5 can only be a factor of a single number, and you can't separate it.)
This shows that there must be a number in ABC that is a multiple of 5, which can be expressed as 5K (k positive integer) must be k = 1 K. if it is not equal to 1, 5K is a composite number, and there are at least two factors besides 1 and 5, which contradicts ABC as a prime number