## Online Course Discussion Forum

### Week 1 Homework assignment questions 3 and 9

Week 1 Homework assignment questions 3 and 9

Does anyone have any ideas/hints how to get started on these?

Re: Week 1 Homework assignment questions 3 and 9

For #3 I would suggest getting a common denominator and using mod arithmetic from there.

I also need some help with #9.

Re: Week 1 Homework assignment questions 3 and 9

So I have (9a^2+14b^2)/b+9a

What do I do from here?

Re: Week 1 Homework assignment questions 3 and 9

Try taking (mod a) and (mod b)

Re: Week 1 Homework assignment questions 3 and 9

I actually got #9 correct (after thinking about it for hours and writing it on my whiteboard multiple times, and maybe writing a python program to do it for me)

My method was setting X and Y to be the base-5 and base-6 counterparts of N, respectively, and setting

N = abc (base 10)

X = defgh (base 5)

Y = jkmn (base 6)

Where the letters denote digits. (i.e. abc could be 243 or 398)

Then from here, remember that

X = 625d + 125e + 25f + 5g + h in decimal

Try converting all of them to decimal.  Remember N=X=Y in decimal!

Try getting an equation that relates c, h, and n, and then use the fact that the last 2 digits of S = the last 2 digits of N.

There are probably better solutions.

This is Charles Zhang, signing off for now.

Re: Week 1 Homework assignment questions 3 and 9

What do you mean by decimal?

By that I mean how does (N=X=Y)?

Re: Week 1 Homework assignment questions 3 and 9

By decimal, I mean base 10 (you know, the base we all count in)

N=X=Y because X and Y are just N written in base 5 and 6, respectively, and converting them back and forth into the same base (most useful would be base 10) will get you the same number.

Take the number in the problem given: 749

N = 749 (base 10)

X = 10444 (base 5)

Y = 3245 (base 6)

N=X=Y in base 10

However, by the way I set up variables,

a=7, b=4, c=9

d=1, e=0, f=4, g=4, h=4

j=3, k=2, m=4, n=5

Then from here, there are some intermediate steps to get the answer.  (Such as equating them by what is given, being careful, and counting possibilities with casework.)

Re: Week 1 Homework assignment questions 3 and 9

Hope this helped!  I am definitely not the best explainer.

Re: Week 1 Homework assignment questions 3 and 9

I definitely took a while for me to understand it.  Sorry for not trying to help earlier.

Re: Week 1 Homework assignment questions 3 and 9

Its fine, I figured it out after I looked at the explanation on AOPS. Thanks for the help, though.