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Old 2018-12-31, 17:34   #144
enzocreti
 
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Default earth shattering discovery

51456=(700^2-164^2)/3^2
541456=(10*700^2-164^2)/3^2
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Old 2018-12-31, 17:43   #145
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Quote:
Originally Posted by enzocreti View Post
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
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Old 2018-12-31, 20:47   #146
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Quote:
Originally Posted by enzocreti View Post
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.
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Old 2019-01-01, 00:14   #147
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Default unbelievable properties of 51456 and 541456

((541456-41)/35+1)/35=442
((51456-41)/35+1)/35=42!!!
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Old 2019-01-01, 00:19   #148
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Default so...

so 51456=35^2*42+6
541456=35^2*442+6!!!
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Old 2019-01-01, 00:35   #149
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Quote:
Originally Posted by enzocreti View Post
((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...)!
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Old 2019-01-01, 00:38   #150
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Quote:
Originally Posted by enzocreti View Post
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.
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Old 2019-01-01, 21:13   #151
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Default 51456 and 541456

51456 and 541456 are remarkably both congruent to 41^2 mod(5^2)
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Old 2019-01-01, 21:18   #152
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even more remarkable is the fact:

(541456-164^2)/10=51456
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Old 2019-01-01, 21:35   #153
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Quote:
Originally Posted by enzocreti View Post
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.
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Old 2019-01-03, 10:25   #154
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Default last but not least...

...int(541456/23)=23541!!!
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