Question

Let \( f \) be a function in two variables defined for natural numbers and
satisfying
1) \( f(x, x) = x \)
2)\( f(x, y) = f(y, x) \)
3)\( (x + y)f(x, y) = y.f (x, x + y) \)
Then find the value of \( f(252, 90) \).

Answer 1

f=0 works
but I suppose you wanted a non-trivial answer...

Answer 2

is it 19/5

Answer 3

sorry , half the way

Answer 4

i dont know but is it 5

Answer 5

The answer is not 5 or 19/5.

Answer 6

2520?

Answer 7

1260 is the answer.

LCM ;)

Answer 8

yay! joemath

Answer 9

Slight variation, what would the answer be if the third rule was:
\[3) f(x,y)=f(x,y-x)\]

Answer 10

sorry Professor Joemath

Answer 11

wait, miss type >.< it should be y+x in the second argument....now that i think about it lol

Answer 12

So third rule:\[f(x,y) = f(x,y+x)\]

Answer 13

GCD isn't ?

Answer 14

8?

Answer 15

yep :) these were interesting problems. Writing out proofs for the solutions were fun.

Answer 16

but foolformath's third rule makes it hard

Answer 17

for me

Answer 18

If you try it with smaller numbers its easier to see.

Answer 19

no really Ishaan, you just don't know (yet) how to tackle these kinds of problems :)

Answer 20

joe is professor ??

Answer 21

im not >.> akshay started calling me that lol. Im a lowly undergraduate.

Answer 22

lol cool man :D

Answer 23

btw joe what about \[ f(x,y)=f(x,y-x) \] ?

Answer 24

ah that was a mistype. although it would lead to the same solution, GCD.

Answer 25

yeah :D