Question

Demonstrați ca nr abc+bca+cab se divide
37​

Answer 1

Explicație pas cu pas:

abc+bca+cab=

100a+10b+c + 100b+10c+a + 100c+10a+b=

100(a+b+c) + 10(a+b+c) + a+b+c=

111(a+b+c)

cum 111:37=3

rezulta ca suma abc+bca+cab se divide la 37

Answer 2

$\displaystyle\it\\\overline{abc}+\overline{bca}+\overline{cab}=(100a+10b+c)+(100b+10c+a)+(100c+10a+b)=\\111a+111b+111c=111(a+b+c)=37\cdot3\cdot(a+b+c) \implies\\37|37\cdot3\cdot(a+b+c).$