# The arithmetic average of four numbers is equal to 34. Find these numbers if it is known that they are directly proportional to four prime natural numbers?

Kavelvyam

381

(to a + to b + to c + d)/4 = 34 a + to b + to c + to d = 34*4 = 8*17 All numbers are proportional to k. a = kp, simple with identical coefficient; b = kq; c = kr; d = ks k * (p + to q + + s) = 8*17 is obvious to r, k = 2, 4 or 8 as the sum of 4 prime numbers cannot be 8. If k = 2, then p + q + r + s = 4*17 = 68 1) 68 = 3 + 5 + 13 + 47; numbers: 6, 10, 26, 94. 2) 68 = 5 + 7 + 13 + 43; number 10, 14, 26, 86. 3) 68 = 3 + 5 + 19 + 41; number 6, 10, 38, 82. 4) 68 = 3 + 5 + 23 + 37; number 6, 10, 46, 74. 5) 68 = 2 + 5 + 31 + 31; number 4, 10, 62, 62. If k = 4, then p + q + r + s = 2*17 = 34 6) 34 = 3 + 3 + 5 + 23; number 12, 12, 20, 92. 7) 34 = 3 + 5 + 7 + 19; number 12, 20, 28, 76 8) 34 = 2 + 2 + 13 + 17; number 8, 8, 52, 68. If k = 8, then p + q + r + s = 17 9) 17 = 2 + 2 + 2 + 11; it is clean 16, 16, 16, 88 10) 17 = 2 + 3 + 5 + 7; number 16, 24, 40, 56. It at first sight - already 10 decisions. If to think the second time, it is possible and to find still.

331

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Pia Katriina

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