ЯсноПонятно24

Простое число r может быть равно 2 или 5.

Для r = 2: 10a + 3b = 2k, a + 8b = 2m 10a + 3b = 2k 10a = 2k - 3b a = (2k - 3b) / 10 a = k/5 - 3b/10 a = k/5 - 3b/10 = m k/5 - 3b/10 = m 2k - 6b = 10m 2k = 6b + 10m 2(k - 3m) = 6b k - 3m = 3b k = 3b + 3m a = k/5 - 3b/10 a = (3b + 3m) / 5 - 3b/10 a = 3b/5 + 3m/5 - 3b/10 a = 3m/5 + b/2 a + 8b = 2m 3m/5 + b/2 + 8b = 2m 3m + 5b + 80b = 10m 5b + 80b = 7m 85b = 7m b = 7m / 85 b = m / 5 a = 3m/5 + b/2 a = 3m/5 + m/10 a = 4m/5 10a + 3b = 2k 10(4m/5) + 3(m/5) = 2k 8m + 3m = 2k 11m = 2k 11m = 2(5n) 11m = 10n m = 10 a = 4m/5 a = 4(10)/5 a = 8 10a + 3b = 2k 10(8) + 3(10) = 2k 80 + 30 = 2k 110 = 2k k = 55 r = 2

Для r = 5: 10a + 3b = 5k, a + 8b = 5m 10a + 3b = 5k 10a = 5k - 3b a = (5k - 3b) / 10 a = k/2 - 3b/10 a = k/2 - 3b/10 = m k/2 - 3b/10 = m 5k - 15b = 10m 5k = 15b + 10m k = 3b + 2m a = k/2 - 3b/10 a = (3b + 2m) / 2 - 3b/10 a = 3b/2 + m - 3b/10 a = 5m/2 - b/2 a + 8b = 5m 5m/2 - b/2 + 8b = 5m 5m - b + 16b = 10m 15b = 5m b = m a = 5m/2 - b/2 a = 5m/2 - m/2 a = 2m 10a + 3b = 5k 10(2m) + 3(m) = 5k 20m + 3m = 5k 23m = 5k 23m = 5(5n) 23m = 25n m = 25 a = 2m a = 2(25) a = 50 10a + 3b = 5k 10(50) + 3(25) = 5k 500 + 75 = 5k 575 = 5k k = 115 r = 5

Итак, подходящими вариантами для r являются 2 и 5.