Question

determinati numerele naturale de forma abc scrise in baza 10, stiind ca are loc egalitatea 2ab+2c=3ab-3c

Answer 1

2ab+2c=3ab-3c

2(10a+b)+2c=3(10a+b)-3c

20a+2b+2c=30a+3b-3c

10a+b-5c=0

10a-5c=-b

b=5c-10a

b=5(c-2a)

Pentru b∈{1,2,3,4,6,7,8,9} nu exista solutii

b=5=>5=5(c-2a)=>1=c-2a=>2a+1=c

a=1=>c=3

a=2=>c=5

a=3=>c=7

a=4=>c=9