Find all positive integers, when divided by 3 leaves remainder 2.
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Dear Student,
Please find below the solution to the asked query:
Dividend=Disvisor×Quotient+RemainderAs m and n leave remainder 2 and 3 respectively when divided by 5, hencem=5x+2 and n=5y+3m2+n2=(5x+2)2+(5y+3)2=25x2+4+20x+25y2+9+30y=25x2+25y2+20x+30y+13=25x2+25y2+20x+30y+10+3⇒m2+n2=5(5x2+5y2+4x+6y+2)+3AsDividend=Disvisor×Quotient+RemainderHence m2+n2 will leave a remainder of 3 when divided by 5.
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