Question

tim so tu nhien n sao cho n :17 du 8 ,n: 25 du16

 

Answer 1

Vì n chia cho 17 dư 8 \(\Rightarrow n+9⋮17\)

Vì n chia cho 25 dư 16 \(\Rightarrow n+9⋮25\)

\(\Rightarrow n+9\in BC\left(17;25\right)\)

Ta có:

\(17=17\)

\(25=5^2\)

\(\Rightarrow BCNN\left(17;25\right)=17.5^2=425\)

\(\Rightarrow BC\left(17;25\right)=B\left(425\right)=\left\{0;425;850;1275;...\right\}\)

\(\Rightarrow n+9\in\left\{0;425;850;1275;...\right\}\)

\(\Rightarrow n\in\left\{416;841;1266;...\right\}\)

Vậy \(n\in\left\{416;841;1266;...\right\}\)

Answer 2

ta có
17 + 8 = 25 
25 + 16 = 41
vậy n = 41