Question

numerele 251,379 si 557 impartite la acelasi nuar natural n,dau resturile 11,19 si respectiv 17.aflati toate valorile lui n

Answer 1

251 : n = x rest 11 ==> nx = 251-11=240
379 : n = y rest 19 ==> ny=379-19=360
557 : n = z rest 17 ==>nz = 557-17 =540

240 = 2^4 × 3 × 5
360 = 2^3 × 3^2 × 5
540 = 2^2 × 3^3 × 5
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2^2 × 3 × 5 = 60
avem conditia n > 19
valorile lui n : 20 ; 30; 60
251 : 20 = 12 rest 11
379 : 20 = 18 rest 19
557 : 20 = 27 rest 17

251 : 30 = 8 rest 11
379 : 30 = 12 rest 19
557 : 30 = 18 rest 17

251 : 60 = 4 rest 11
379 : 60 = 6 rest 19
557 : 60 = 9 rest 17