1.

Prove that 2222^(5555)+5555^(2222) is divisible by 7

Answer»

Solution :When 2222 is divided by 7 it leaves a reminder 3
So adding & SUBTRACTING `3^(5555)` we get

For `E_(1)` : Now since 2222-3 =2219 is divideble by 7 thefore `E_(1)` is dividible by 7 `
(`thereforex^n - a^n ` is divisible by x - a)
For `E_2:555 when devided by 7 leaves remainder 4ltbegt Soadding and subtracting `4^(2222)` we get
`E_(2)=3^(5555)+4^(2222)+5555^(2222)-4^(2222)`
`= (243)^(1111)+(16)^(1111)+5555^(2222)- 4^(2222)`
`=(243)^(1111)+(16)^(1111)+(5555)^2222-4^(2222)` are divisible by7


Discussion

No Comment Found

Related InterviewSolutions