Question

Suma numerelor de forma abcd (abcd numar din 4 cifre) ce satisface relatia abcd+ab*cd-97ab=2010 (toate au bara deasupra)

Answer 1

abcd +ab•cd-97•ab=2010

ab•100+cd+ ab•cd-97•ab=2010

ab(100+cd-97)+cd=2010

ab(cd+3) +cd=2010        +3

ab(cd+3) +cd+3=2013

(cd+3)(ab+1)=2013

(ab+1)(cd+3)=3•11•61

ab si cd sunt numere de 2 cifre

=> (ab+1)(cd+3)=33•61=61•33

ab+1=33 si cd+3=61 => ab=32 si cd=58 => abcd=3258

ab+1=61 si cd+3=33 => ab=60 si cd=30 => abcd=6030

=> 3258+6030=9288