Question

find a formula for the position of \(p^xq^y\) in the below increasing sequence \[\large \{p^aq^b : a,b=0,1,2\ldots\}\]

where \(p\lt q\) are primes

Answer 1

could you explain more or give example ?

Answer 2

can you please help on my last question??

Answer 3

Is p and q fixed or is it a variable?

Answer 4

i think \(p, q\) are fixed

Answer 5

they could be any fixed primes, for exampel :

(p, q) = (3, 5)
or
(p, q) = (13, 23)

Answer 6

it is only given that they are different primes and the sequence is increasing

Answer 7

wunt it just be p^a*q^b

Answer 8

for (p, q) = (3, 5),

the position of p^0q^0 is 1
the position of p^1q^0 is 2
the position of p^0q^1 is 3
theposition of p^2q^0 is 4
the position of p^1q^1 is 5

etc...

Answer 9

ohh i gotcha!

Answer 10

lets see if we can come up with a function including the diff between primes

Answer 11

these kinda questions are interesting

Answer 12

these are bit hard too... been trying this from couple of days on and off

Answer 13

now we shud have a function based off binomial expansion

Answer 14

ah gonna rewtite