Explicație pas cu pas:
a = 5^(5n+7)
b = 3^(5m+4)
m, n sunt numere naturale
25ab = 25 × 5^(5n+7) × 3^(5m+4) =
= 5^(5n+9) × 3^(5m+4) ==>
==> 25ab are (5n+10)(5m+5) divizori ==>ab are (5n+8)(5m+5) divizori
(5n+10)(5m+5) = 40 + (5n+8)(5m+5)
(5m+5)(5n+10-5n-8) = 40
(5m+5) × 2 = 40
5m + 5 = 20
5m = 15
m = 3 ==> b = 3^19
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9ab = 9×5^(5n+7) × 3^(5m+4) =
= 5^(5n+7) × 3^(5m+6) ==>
==> 9ab are (5n+8)((5m+7) divizori
ab = are (5n+8)(5m+5) divizori
==> (5n+8)(5m+7) = 36+ (5n+8)(5m+5)
(5n+8)(5m+7-5m-5) = 36
(5n+8) × 2 = 36
5n+8 = 18
5n = 18-8=10
n = 2 ==> a = 5^17
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