541456 and 51456. I checked 20 numbers 2000 times and found 200 patterns!! - Page 14

enzocreti · 2018-12-31, 17:34

51456=(700^2-164^2)/3^2
541456=(10*700^2-164^2)/3^2

science_man_88 · 2018-12-31, 17:43

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

Batalov · 2018-12-31, 20:47

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.

enzocreti · 2019-01-01, 00:14

((541456-41)/35+1)/35=442
((51456-41)/35+1)/35=42!!!

enzocreti · 2019-01-01, 00:19

so 51456=35^2*42+6
541456=35^2*442+6!!!

chalsall · 2019-01-01, 00:35

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...)!

science_man_88 · 2019-01-01, 00:38

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.

enzocreti · 2019-01-01, 21:13

51456 and 541456 are remarkably both congruent to 41^2 mod(5^2)

enzocreti · 2019-01-01, 21:18

even more remarkable is the fact:

(541456-164^2)/10=51456

science_man_88 · 2019-01-01, 21:35

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.

enzocreti · 2019-01-03, 10:25

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

2018-12-31, 17:34	#144
enzocreti Mar 2018 1022₈ Posts	earth shattering discovery 51456=(700^2-164^2)/3^2 541456=(10*700^2-164^2)/3^2

2019-01-01, 00:14	#147
enzocreti Mar 2018 2×5×53 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 1000010010₂ Posts	so... so 51456=35^242+6 541456=35^2442+6!!!

2019-01-01, 21:13	#151
enzocreti Mar 2018 2·5·53 Posts	51456 and 541456 51456 and 541456 are remarkably both congruent to 41^2 mod(5^2)

2019-01-03, 10:25	#154
enzocreti Mar 2018 2·5·53 Posts	last but not least... ...int(541456/23)=23541!!!

2019-01-01, 21:18	#152
enzocreti Mar 2018 2×5×53 Posts	even more remarkable is the fact: (541456-164^2)/10=51456

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