Question

Determinati numerele naturale de patru cifre care se micsoreaza cu 2916 daca ultima cifra se muta in fata numarului.
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Answer 1

Răspuns:

abcd={4351, 5462, 6573, 7684, 8795, 9906}

Explicație pas cu pas:

abcd=dabc+2916

abc*10+d=d*1000+abc+2916

10*abc-abc=1000*d-d+2916

9*abc=999*d +2916     /:9

abc=111*d+324

d=1 =>abc=111+324

abc=435=> abcd=4351

V: 4351=1435+2916

d=2 => abc=222+324

abc=546=> abcd=5462

V: 5462+2546+2916

d=3=> abc=333+324

abc=657=> abcd=6573

V: 6573=3657+2916

d=4=> abc=444+324

abc=768=> abcd=7684

V: 7684=4768+2916

d=5=> abc=555+324

abc=879=> abcd=8795

V: 8795=5879+2916

d=6=> abc=666+324

abc=990=> abcd=9906

V: 9906=6990+2916

abcd={4351, 5462, 6573, 7684, 8795, 9906}