There is a 5 - digit number 10**0 , when this number divided by 23 or 29, both will get a remainder of 5. What is the value of this integer?
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31 tháng 12 2016
Call a is the 3-digit number which divied by 57, the remainder is 27, divided by 217, the remainder is 60.
\(\Rightarrow\)a-27\(⋮\)57
\(\Rightarrow\)a-60\(⋮\)217
Because 684 is a multiple of 57 so:
\(\Rightarrow\)a-27-684\(⋮\)57\(\Rightarrow\)a-771\(⋮\)57
Because 651 is a multiple of 217 so:
\(\Rightarrow\)a-60-651\(⋮\)217\(\Rightarrow\)a-771\(⋮\)217
\(\Rightarrow\)a-771 \(\in\)CM(217;57)
\(\Rightarrow\)a-771\(\in\){0;12369;...}
\(\Rightarrow\)a\(\in\){771;13140;...}
Because a is a 3-digit number so a = 771.
The number is 771.