The number of non negative integral solutions of the equation x+y+2z=33
#solution
tulip coral
dusk fossilBOT
The number of non negative integral solutions of the equation x+y+2z=33
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tulip coral
Anyone???
distant nimbus
general hint
if you wanna solve x+y=N you have solutions like (0,N), (1,N-1), (2,N-2) etc
how many are there?
for x+y+2z = 33, fix a possible value of z and solve x+y = 33-2z as before
e.g z=0 has you solve x+y=33, z=1 x+y=31 etc
@tulip coral
tulip coral
e.g z=0 has you solve x+y=33, z=1 x+y=31 etc
when z=1
So i am getting sum
34+32+30+28+.....0
distant nimbus
There was a formula can I not apply it here?<@215155833036734465>
there are a million formulas
tulip coral
Max z is 16
distant nimbus
when is this formula true?
tulip coral
x+y+z=33
Then it is true i guess
33+3-1C2
35C2
2+4+6+8+....34
I got 306
@distant nimbus
Stop laughing please 😭😂😂😂😂😂
distant nimbus
if it is true, then prove it
distant nimbus
the formula you were talking aboutä
tulip coral
No formula doesn't work here. It works only for the i guess
Let me count it and check
306 is correct?
@distant nimbus
Formula works fine here
Bro see
@distant nimbus
wanton kestrel
the coefficient of v^33 in the expansion of 1/[(1-v)^2 (1-v^2)] near 0
$\underbrace{(v^0+v^1+v^2+\ldots)}{x} \underbrace{(v^0+v^1+v^2+\ldots)}{y}\underbrace{(v^0+v^2+v^4+\ldots)}_{z}$
alpine surgeBOT
Heavily cooked
tulip coral
the coefficient of v^33 in the expansion of 1/[(1-v)^2 (1-v^2)] near 0
Interesting
Where did you get the idea?
wanton kestrel
from the problem
tulip coral
I saw a same comment on math exchange
wanton kestrel
gfs are very common in this territory
tulip coral
gfs?
wanton kestrel
generating functions
wanton kestrel
The number of non negative integer solutions to ax_1 + bx_2 + cx_3 +... = n where a, b, c,... are integers is the coefficient of x^n in 1/[(1-x^a)(1-x^b)(1-x^c)...]
wanton kestrel
if a_1, a_2,...,a_k are coprime then the number of solutions to a_1 x_1 +...+ a_k x_k = n is ~ k^n/[(n-1)!a_1 a_2...a_k]
it helps if n is huge
tulip coral
+close