#### Topic: How to find all?

To find all numbers in decimal numeration with such property: if decimal digits of number to write down upside-down, the same number, only in hexadecimal system turns out. For double-valued numbers: a*10+b=b*16+a ==> a*9=b*15 ==> a = b*5/3 ==> b=3 and =5. Guards that in a statement of the problem it is told "to Find all numbers..." The question: 1) whether there is any upper bound for numbers which satisfy a search criterion; 2) whether there is any numerical regularity for the task decision?

#### Re: How to find all?

Hello, olimp_20, you wrote: _> to Find all numbers in decimal numeration with such property: if decimal digits of number to write down upside-down, the same number, only in hexadecimal system turns out. _> for double-valued numbers: a*10+b=b*16+a ==> a*9=b*15 ==> a = b*5/3 ==> b=3 and =5. _> Guards that in a statement of the problem it is told "to Find all numbers..." _> [i] the Question: 1) whether there is any upper bound for numbers which satisfy a search criterion; Start up length of considered number n discharges. Then should be: 1*16 ^ (n-1) <= 9*10 ^ (n-1) * 2 since hexadecimal numbers even with 1 in the high order increase faster at growth of number of discharges, than decimal with 9 in the senior.

#### Re: How to find all?

Hello, lpd, you wrote: lpd> Start up length of considered number n discharges. Then should be: 1*16 ^ (n-1) <= 9*10 ^ (n-1) * 2 since hexadecimal numbers even with 1 in the high order increase faster at growth of number of discharges, than decimal with 9 in the senior. And what hinders number to have in the end zero?