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 2018-12-31, 17:34 #144 enzocreti   Mar 2018 10000011112 Posts earth shattering discovery 51456=(700^2-164^2)/3^2 541456=(10*700^2-164^2)/3^2
2018-12-31, 17:43   #145
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

100000110000002 Posts

Quote:
 Originally Posted by enzocreti 51456=(700^2-164^2)/3^2 541456=(10*700^2-164^2)/3^2
not really surprising since (700^2-164^2)/3^2+700^2 = (700^2-164^2)/3^2 + (9*700^2)/3^2= (700^2-164^2+9*700^2)/3^2 = (10*700^2-164^2)/3^2

2018-12-31, 20:47   #146
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

100100101011012 Posts

Quote:
 Originally Posted by enzocreti earth shattering discovery 51456=(700^2-164^2)/3^2 541456=(10*700^2-164^2)/3^2
You should play number games more frequently, like the usual New Year's four-digit jam (I've played similar jams since something like 1976...)

You can make an expression for almost any number using surprisingly few digits.

 2019-01-01, 00:14 #147 enzocreti   Mar 2018 52710 Posts unbelievable properties of 51456 and 541456 ((541456-41)/35+1)/35=442 ((51456-41)/35+1)/35=42!!!
 2019-01-01, 00:19 #148 enzocreti   Mar 2018 20F16 Posts so... so 51456=35^2*42+6 541456=35^2*442+6!!!
2019-01-01, 00:35   #149
chalsall
If I May

"Chris Halsall"
Sep 2002

3·52·127 Posts

Quote:
 Originally Posted by enzocreti ((51456-41)/35+1)/35=42!!!
My goodness!!! You're correct! That's amazing! 42!

Amoungst other things, it's the Answer to the Ultimate question of Life, the Universe and Everything (unfortunately, no one remembers what the question was...)!

2019-01-01, 00:38   #150
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 Originally Posted by enzocreti so 51456=35^2*42+6 541456=35^2*442+6!!!

here's a list of numbers they have equal remainder on division by:

Code:
1,2,4,5,7,8,10,14,16,20,25,28,35,40,49,50,56,70,80,98,100,112,125,140,175,196,200,245,250,280,350,392,400,490,500,560,625,700,784,875,980,1000,1225,1250,1400,1750,1960,2000,2450,2500,2800,3500,3920,4375,4900,5000,6125,7000,8750,9800,10000,12250,14000,17500,19600,24500,30625,35000,49000,61250,70000,98000,122500,245000,490000
So again it's no surprise. Please do some actual mathematics.

 2019-01-01, 21:13 #151 enzocreti   Mar 2018 17·31 Posts 51456 and 541456 51456 and 541456 are remarkably both congruent to 41^2 mod(5^2)
 2019-01-01, 21:18 #152 enzocreti   Mar 2018 10178 Posts even more remarkable is the fact: (541456-164^2)/10=51456
2019-01-01, 21:35   #153
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

203008 Posts

Quote:
 Originally Posted by enzocreti even more remarkable is the fact: (541456-164^2)/10=51456
no it's not:

This is a way a proof can look, please prove something about pg(k) specifically.

 2019-01-03, 10:25 #154 enzocreti   Mar 2018 17×31 Posts last but not least... ...int(541456/23)=23541!!!

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