If M and N are prime numbers, and the positive integers K and t satisfy K + T = m, K times t = n, then the n power of M + the m power of N + the t power of K + the K power of T =?

If M and N are prime numbers, and the positive integers K and t satisfy K + T = m, K times t = n, then the n power of M + the m power of N + the t power of K + the K power of T =?

N is a prime number, KT is a positive integer, K, t must have one equal to N, the other is 1, we can get the n power of M + m power of N + T power of K + K power of T = n power of M + m power of N + N + 1; K + T = M = n + 1; only 2,3 of all prime numbers satisfy, we can get m = 3, n = 2;
N power of M + m power of N + T power of K + K power of T = 9 + 8 + 2 + 1 = 20

It is known that a + B + C = 2, A2 + B2 + C2 = 2. It is proved that the range of a, B, C is 0 to 4 / 3

(2-c)^2=(a+b)^2

If the real numbers a, B and C satisfy a + 2B + 3C = 12 and A2 + B2 + C2 = AB + AC + BC, then the value of a + B2 + C3 is______ ．

∵ A2 + B2 + C2 = AB + AC + BC, {2A2 + 2B2 + 2c2 = 2Ab + 2Ac + 2BC, {(a2-2ab + B2) + (a-2ac + C2) + (b2-2bc + C2) = 0, {(a-b) 2 + (A-C) 2 + (B-C) 2 = 0, ∵ A-B = 0, a-c = 0, B-C = 0, namely a = b = C, and ∵ a + 2B + 3C = 12, ∵ a = b = C = 2, ∵ a + B2 + C3 = 2 + 4 + 8 = 14