[/quote]
,
,
and the function 
defined by![\[f(n)=\left\lfloor \frac{an+b}{cn+d}\right\rfloor\text{ for all } n\in\mathbb{Z}_{\ge 0}.\]](http://latex.artofproblemsolving.com/8/f/b/8fb372df4b44c3d7c0690b310b12c684134fee74.png)
Prove that the following are equivalent:
is surjective;
,
and 
.
given that there exist positive integers 
satisfying
and 
.
and 
. Prove that
Where 
that satisfied
such that![\[
f(f(x)) + x f(xy) = x + f(y)
\]](http://latex.artofproblemsolving.com/9/1/5/9157eb92f89f6c96333ce105a88ebed02c5307ef.png)
for all positive real numbers 
and 
.
)
has circumcenter 
.
and 
intersect at 
,
and 
intersect at 
and 
and 
intersect at 
.
are similar(with vertices in that order), than 
,
and 
and 
,
and 
.
and 
.
such that ![\[f(f(x)) + xf(xy) = x + f(y)\]](http://latex.artofproblemsolving.com/a/6/f/a6f84dd53eec985b90bad3df6580eeaf29d73195.png)
for all positive real numbers 
and 
.
Y by MathPerson12321, DhruvJha, Soupboy0, Andyluo, evt917, Eddie_tiger, aidan0626, pingpongmerrily, JackieWacky, rayquaza7, PhoenixMathClub, sm100, PikaPika999, Math-Learner99
Previous Years' "Hubs": (2022) (2023) (2024)
Now that it's April and we're allowed to discuss ...
* means that CDR is official in that state.
For those asking about the removal of the tiers, I'd like to quote Jason himself:
Help contribute by sharing your state's cutoffs!
Now that it's April and we're allowed to discuss ...
- CA: 43 (45 44 43 43 43 42 42 41 41 41)
- NJ: 43 (45 44 44 43 39 42 40 40 39 38) *
- NY: 42 (43 42 42 42 41 40)
- TX: 42 (43 43 43 42 42 40 40 38 38 38)
- MA: 41 (45 43 42 41)
- WA: 41 (41 45 42 41 41 41 41 41 41 40) *
- VA: 40 (41 40 40 40)
- FL: 39 (42 41 40 39 38 37 37)
- IN: 39 (41 40 40 39 36 35 35 35 34 34)
- NC: 39 (42 42 41 39)
- IL: 38 (41 40 39 38 38 38)
- OR: 38 (44 40? 38 38)
- PA: 38 (41 40 40 38 38 37 36 36 34 34) *
- MD: 37 (43 39 39 37 37 37)
- AZ: 36 (40? 39? 39 36)
- CT: 36 (44 38 38 36 35 35 34 34 34 33 33)
- MI: 36 (39 41 41 36 37 37 36 36 36 36) *
- MN: 36 (40 36 36 36 35 35 35 34)
- CO: 35 (41 37 37 35 35 35 ?? 31 31 30) *
- GA: 35 (38 37 36 35 34 34 34 34 34 33)
- OH: 35 (41 37 36 35)
- AR: 34 (46 45 35 34 33 31 31 31 29 29)
- NV: 34 (41 38 ?? 34)
- WI: 34 (40 37 37 34 35 30 28 29 29 29) *
- HI: 32 (35 34 32 32)
- NH: 31 (42 35 33 31 30)
- DE: 30 (34 33 32 30 30 29 28 27 26? 24)
- SC: 30 (33 33 31 30)
- IA: 29 (33 30 31 29 29 29 29 29 29 29 29 29) *
- NE: 28 (34 30 28 28 27 27 26 26 25 25)
- SD: 22 (30 29 24 22 22 22 21 21 20 20)
* means that CDR is official in that state.
For those asking about the removal of the tiers, I'd like to quote Jason himself:
peace09 wrote:
learn from my mistakes
Help contribute by sharing your state's cutoffs!
This post has been edited 72 times. Last edited by SirAppel, Apr 8, 2025, 8:49 PM
