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1d
comment Find the values of a and b so the system shown has the solution (2,3). Does the system have any other solutions? Explain.
What have you tried to solve this, Bekah?
1d
comment For which values of $a$ does this equation have a solution(s)?
Could you edit the question to give us more detail of what you've done in terms of getting a quadratic and so forth please?
1d
comment For which values of $a$ does this equation have a solution(s)?
Did you check to see where the discriminant of the quadratic would be positive?
Apr
17
comment What is the remainder of $314^{164}$ divided by 165?
You use the CRT to combine the congruences, e.g. 1 mod 3 and 1 mod 5 would be 1 mod 15.
Apr
14
comment Which of this two numbers is the bigger?
What if $x=0$? Then the inequality isn't correct.
Apr
13
comment Writing numbers as a sum of 2s and 3s
Depending on the number, the key is to be able to reduce it to a multiple of 6 so that then there are a couple of different combinations to note as a triple set of 2s would produce a 6 as would a double set of 3s. Thus, 8 and 9 for example each have 2 possibilities: 2+2+2+2=3+3+2 for 8 while 9 is 2+2+2+3=3+3+3. This would apply for 8,9,10,and 11. For 12, one could see this as a double of the 6 case and so one could use all 2s, partially use 2s or use no 2s for the 3 possibilities here. Integers of the form $6k+1$ are a bit special to handle differently of course but a pattern does exist.
Apr
13
comment Writing numbers as a sum of 2s and 3s
Given that 6 can be written as a sum of three 2s or as two 3s, wouldn't this substitution be the key point to consider in recursively finding all pairs that would work?
Apr
13
answered What does inversion mean?
Apr
13
comment Why descend from a hill is not measured negative?
How would you interpret an answer of $-5$ days?
Apr
9
answered What is the following expression simplified to?
Apr
4
comment Can this congruence be reduced?
Is $(x+1)^2-1$ really the solution for $y$ or could there be more than that?
Apr
4
comment Can this congruence be reduced?
en.wikipedia.org/wiki/Zero_divisor explains the concept that is worth noting as usually in algebra if $a^2=0$ then $a=0$ is given as a consequence which in this case would mean there is a reduction to $x\equiv-1 mod (y+1)$
Apr
4
comment Can this congruence be reduced?
Are there zero divisors mod (y+1)? For example, mod 4, the solutions would be 1 and 3 mod 4 for x as 0 can be squared but so can 2 in this special case of $y+1=p^2$.
Apr
2
comment How to check if $2$ is a square $\mod 3$?
@EYES, what other numbers exist mod 3? 0,1, and 2 are the only numbers here.
Apr
1
comment how many ways you can take 4 integers from the N numbers such that their GCD is 1
If all subsets with exactly 4 elements have a GCD of 1 then the answer is 5 choose 4 which is 5 since it is a matter of considering which integer is missing. Course if all 5 integers share a common factor greater than 1 then the answer is 0. For example if the numbers were 2 4 8 16 32, then there isn't any set that would work.
Apr
1
comment how many ways you can take 4 integers from the N numbers such that their GCD is 1
Do you know any properties of the numbers? For example, if I choose for the same n=5 the numbers 2,3,5,7,11 then the answer will be 5 choose 3 whereas in your example the calculation is 4 choose 3 as 1 with any 3 other numbers will work and the other 4 values have a common factor of 2.
Apr
1
comment How many 5-permutations of Q are there? (No repetition of character within a string and order matters)
No, that is the formula if order doesn't matter as one is going to use all the characters so there is only one combination.
Apr
1
comment Which Logical Fallacy Is Used?
Misdirection would be my initial thought.
Mar
31
awarded  Yearling
Mar
26
comment Why do we keep the LCM modulo in the Chinese Remainder Theorem?
Consider which is more strict by looking at a few values that satisfy one but not the other.