IIT JEE , AIEEE Forum - Mathematics , Algebra

sboosy

7¹ is 7 ..that is it ends with 7

7² is 49 ..ends with 9

7³ ends with 3

7⁴ ends with 1

after this it starts repeating

now comparing ending numbers

power 1 goes with 3 ..so that its divisible by 5

power 2 goes with 4 so that its divisible by 5

so if we see this way

take x to be 1

y can b 3 or 7 or 11 or ..just keep addin 4 ....until 99

so 25 numbers

take x to be 3

y can be 5 or 9 or ....97 ...so 24 numbers

in this way we get

25+24+23+ ....1

but this is for odd alone

similarly when x is 2

y can be 4 or 8 or 12 ..100 ...25 numbers

next 24 ...

so again we get

25+24+23+....1

but x and y can commute

so it is 4 (1+2+3+...25) / 100C₂

= 4 (25*26/2) / 100C₂

pls correct if i made any calculation mistake