Question

Dau coroana si 20 de puncte! ​

Answer 1

2•abcd=19•(acd-2)

2000a+200b+2·cd=1900a+19•cd-38

2000a-1900a+200b=19•cd-2•cd-38

100a+200b=17•cd-38

100(a+2b)=17•cd-38

ultimele doua cifre ale diferentei 17•cd-38 sunt 00=> ultimele doua cifre ale produsului 17•cd=38

u(17•cd)=8=> d=4

17•(10c+4)=170c+17•4=170c+68

doar pentru c=1=> 170+68=238; ultimele 2 cifre sunt 38

deci, cd=14

=> 100(a+2b)=17•14-38

100(a+2b)=238-38

100(a+2b)=200  /:100

a+2b=2; a≠0

=> a=2 si b=0

abcd=2014

verificare: 2•2014=19•(214-2)

                  4028=19•212  (A)