Question

Chứng minh rằng nếu số tự nhiên 𝑎𝑏𝑐 ⋮37thì các số 𝑏𝑐𝑎 và 𝑐𝑎b cũng chia hết cho 37.

Answer 1

\(\overline{abc}⋮37\Rightarrow100a+10b+c⋮37\\ \Rightarrow1000a+100b+10c⋮37\\ \Rightarrow1000a-999a+100b+10c⋮37\left(999a⋮37\right)\\ \Rightarrow100b+10c+a⋮37\\ \Rightarrow\overline{bca}⋮37\)

 

Answer 2

\(\overline{abc}⋮37\Rightarrow100a+10b+c⋮37\\ \Rightarrow10000a+1000b+100c⋮37\\ \Rightarrow10000a-9990a+1000b-999b+100c⋮37\left(9990a⋮37;999⋮b\right)\\ \Rightarrow100c+10a+b⋮37\\ \Rightarrow\overline{cab}⋮37\)