ka April Highlights and 2025 AoPS Online Class Information
jlacosta0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.
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It is May 1st. I have been anticipating the arrival of my results displayed in the awards ceremony in the form of a digital certificate. I have unfortunately not received anything. I have heard from other sources(AoPS, and the internet), that the certificates generally arrive at the end of the month. I would like to ask the organizers, or the coordinators of the tournament, to at least give us an ETA. I would like to further elaborate on the expedition of the release of the Question Papers and the grading. The question papers would be very helpful to the people who have taken the contest, and also to other people who would like to solve them. It would also help, as people can discuss the problems that were given in the test, and know different strategies to solve a problem they have solved. In regards to the grading, it would be a crucial piece of evidence to dispute the score shown in the awards ceremony, in case the contestant is not satisfied.
This has been going on for a while now, can anyone else relate?
jmr20102
NYesterday at 3:02 AM
by valisaxieamc
Most of the time when I type in something for the tags or search for a user, the AoPS suggestion box pops up, and most of the time, when I click the suggestion, the box just disappears, meaning the automatic system usually never works
hi. my aops whenever i go 2 the website the website is like way to big and i cant access anything? i am on via an ingognito window but its kind of inconvenient not sure if its just my laptop or the website. i cant recreat it on any other device? plz help [/resolved]
4 some reason alcumus isnt working??? in the 1st attachment there isnt any "play, profile, ...etc."
and in the second pic i clicked the "play" button, but its just a blank screen??? i tried refreshing it didnt work????
This started today.
When I tried to type in the AoPS homework section (as well as forums), where you put your answers into the slots, I found that I couldn’t? This might only be my device but it was delaying my work and I just thought I’d share.
I refreshed multiple times, but it only works sometimes.
Sometimes, the blinking blue bar shows but I can’t type, and other times, the blue bar doesn’t show at all.
I am able to type this forum up since this was one of the few times that my device let me type (for more, I have an iPad. Not sure what generation, but it’s a pretty recent version, I believe).
If this is a problem with my device, I apologize for wasting your time :)
Just wanted to make sure I could get this notice out if others have the same problem.
Converting from base to base 10, we get for a postive integer because its a divisor. Then you can simplify this to and since n or b cant be negative that means n has to be from 1 to 9 exclusive. Then casework from 2-8, and u get n=7 then b=21 and n=8 then b=40 so its 70
First, note that so it follows that must be a divisor of The only divisors of greater than are and so it follows that the possible values of are and yielding an answer of
9b+7 is divisible by b+7, so 9b+7 - 9(b+7) will still be divisible by b+7, so -56 is divisible by b+7. we first try -56-7=-49, so one b possibility could be 49. 49-7=42, 42/2 = 21, 21 is another possibility. 21-7=14, 14/2 = 7, which is less than 9, so we only have 21 and 49, giving us 70.
By the definition of a divisor, for an integer . Clearly does not work. So now we can just try every single value.
no gives which doesn't work gives which doesn't work gives which doesn't work gives which doesn't work gives which doesn't work gives which does work gives which does work
By the definition of a divisor, for an integer . Clearly does not work. So now we can just try every single value.
no gives which doesn't work gives which doesn't work gives which doesn't work gives which doesn't work gives which doesn't work gives which does work gives which does work
I was stuck on this problem for some reason I don't know why
The best way to tackle this problem is to convert everything to variables so first 17 base b = b + 7 and 97 base b = 9b+7 so we can just make a variable when multiplied by it it equals 97 base b
So first to do that we can simplify it like 9b+7 = x(b+7) for some value of x then when we multiply that out we get 9b+7=bx+7x. Because we want to solve for xb we have to subtract that on both sides to get 9b+7-bx= 7x then in any situation like this we have to factor out the b, but first we can subtract 7 on both sides.
When we do that we get b(9-x)= 7(x-1) which when we divide both sides we get
b= (7(x-1))/(9-x) we get this easy equation to solve because we know that x has to be a single digit number because anything greater than 9 won't work so we get that after guess and check x= 7 and 8 so when we plug that in we get 21 and 49, so when we add those together you get
This post has been edited 2 times. Last edited by sadas123, Feb 9, 2025, 4:44 PM
b+7 is divisible by 9b+7, but because b+7 is divisible by 9b+63, then b+7 is divisible by 56. And B+7 is greater than 7, so b=21 or 49[Click][sounds stupid but I got b+7 is divisible by 8b, and did a lot of stupid stuff to get -6+-5+-3+0+1+7+21+49=64 cause I forgot b is greater than 9, but luckily I realized this at the end.]
Find the sum of all integer bases for which is a divisor of
We need , so . Let , do casework and bounding.
If then so , doesn't work.
If then so , doesn't work.
If then so , which does work.
If then so , which does work.
If then so , doesn't work.
Our answer is .
(97)b =9b+7
(17)b=b+7
So b+7 divides 9b+7
gcd(9b+7,b+7)=b+7
gcd(-56,b+7)=b+7
So we get b+7 divides -56
Now , 56=2*2*2*7 and factors greater than 9+7 are 28 and 56 itself
So, b=21 or 49
Sum =70(answer)