We use cookies to ensure you have the best browsing experience on our website. Please read our cookie policy for more information about how we use cookies.
Keywords: primes up to , heap, set or dict of seen values, list of prime exponents. For example, 130754415038 should results in 307916385330322622578697205433200 ([4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) instead of 1602387094135655108133744107956740 ([2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]).
You should find all x,y that verify the given equation and give the number of the solution just note that (x,y) and (y,x) are considered one solution.
Start first by finding the writing of X and Y using arithmetics
As per Algo description, n=1260 than we will have 113 distinct solution, what are those value of solution and what are x and y value which cover 113 possiblity. need small example if possible
these are some example for n=8
we should find all x,y that verify x*y/(x+y)=8
And we get (9,8*9)
(2*6,4*6)
(4*6,2*6)
(8*9,9 )
(2*5,8*5)
(4*4,4*4)
(8*5,2*5)
(4*3,8*3)
(8*3,4*3)
(8*2,8*2)
By removing none distinct
We get
(9,8*9)
(2*6,4*6)
(2*5,8*5)
(4*4,4*4)
try to find x,y using arithmetic
1/1261+1/1588860,1/1262+1/795060,1/1263+1/530460,1/1264+1/398160,1/1265+1/318780,1/1266+1/265860,1/1267+1/228060,1/1269+1/177660,1/1270+1/160020,1/1272+1/133560,1/1274+1/114660,1/1275+1/107100,1/1278+1/89460,1/1280+1/80640,1/1281+1/76860,1/1288+1/57960,1/1290+1/54180,1/1295+1/46620,1/1296+1/45360,1/1302+1/39060,1/1305+1/36540,1/1320+1/27720,1/1323+1/26460,1/1330+1/23940,1/1344+1/20160,1/1350+1/18900,1/1365+1/16380,1/1386+1/13860,1/1400+1/12600,1/1440+1/10080,1/1470+1/8820,1/1512+1/7560,1/1575+1/6300,1/1680+1/5040,1/1890+1/3780,1/2520+1/2520. Ok, they are actually only 36 !?
try solving Diophantine reciprocals I,you'll find that there are 113 solution for 1260. NB: 36 is only the number of multiples of 1260. If you apply the same logic to 8 you wont find the solutions i gave above
Value for 10^13 is: n = 11620062538285412860755634822552050592800
Keywords: primes up to ,
heap,setordictof seen values,listof prime exponents. For example,130754415038should results in307916385330322622578697205433200([4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) instead of1602387094135655108133744107956740([2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]).can u add more information which help me to understand the issue
You should find all x,y that verify the given equation and give the number of the solution just note that (x,y) and (y,x) are considered one solution. Start first by finding the writing of X and Y using arithmetics
As per Algo description, n=1260 than we will have 113 distinct solution, what are those value of solution and what are x and y value which cover 113 possiblity. need small example if possible
these are some example for n=8 we should find all x,y that verify x*y/(x+y)=8 And we get (9,8*9) (2*6,4*6) (4*6,2*6) (8*9,9 ) (2*5,8*5) (4*4,4*4) (8*5,2*5) (4*3,8*3) (8*3,4*3) (8*2,8*2) By removing none distinct We get (9,8*9) (2*6,4*6) (2*5,8*5) (4*4,4*4) try to find x,y using arithmetic
1/1261+1/1588860,1/1262+1/795060,1/1263+1/530460,1/1264+1/398160,1/1265+1/318780,1/1266+1/265860,1/1267+1/228060,1/1269+1/177660,1/1270+1/160020,1/1272+1/133560,1/1274+1/114660,1/1275+1/107100,1/1278+1/89460,1/1280+1/80640,1/1281+1/76860,1/1288+1/57960,1/1290+1/54180,1/1295+1/46620,1/1296+1/45360,1/1302+1/39060,1/1305+1/36540,1/1320+1/27720,1/1323+1/26460,1/1330+1/23940,1/1344+1/20160,1/1350+1/18900,1/1365+1/16380,1/1386+1/13860,1/1400+1/12600,1/1440+1/10080,1/1470+1/8820,1/1512+1/7560,1/1575+1/6300,1/1680+1/5040,1/1890+1/3780,1/2520+1/2520. Ok, they are actually only 36 !?
try solving Diophantine reciprocals I,you'll find that there are 113 solution for 1260. NB: 36 is only the number of multiples of 1260. If you apply the same logic to 8 you wont find the solutions i gave above
what are x and y's?
X and Y are two integers
to be precise, they are positive integers.