Numbers 99,000,000,000s

99,049,307,841

[Math.]  (1+2+…+33)4 = [(15+25+…+335)+(17+27+…+337)]/2.

 

99,112,262,041

[Math.]  Sum of the first 793 cube numbers:

13+23+…+7933 =  99,112,262,041 = (1+…+793)2 = 314,8212.

 

99,612,828,225

[Math.]  Sum of the first 794 cube numbers:

13+23+…+7943 =  99,612,828,225 = (1+…+794)2 = 315,6152.

 

99,876,654,332

[Math.]  

296×333,667 = 98,765,432

2,996×33,336,667 = 99,876,654,332

29,996×3,333,366,667 = 99,987,666,543,332

299,996×333,333,666,667 = 99,998,766,665,433,332

2,999,996×33,333,336,666,667 = 99,999,876,666,654,333,332

29,999,996×3,333,333,366,666,667 = 99,999,987,666,666,543,333,332

299,999,996×333,333,333,666,666,667 = 99,999,998,766,666,665,433,333,332

2,999,999,996×33,333,333,336,666,666,667 = 99,999,999,876,666,666,654,333,333,332 

29,999,999,996×3,333,333,333,366,666,666,667 =  99,999,999,998,766,666,666,663,333,333,332

299,999,999,996×333,333,333,333,366,666,666,667 = 99,999,999,998,766,666,666,665,433,333,333,332

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99,961,946,721

[Math.]  The largest 11-digit cube number = 46413.

 

99,991,100,003

[Math.]  A prime number, formed by 2 consecutive prime numbers 99991 and 100003.

 

99,994,257,363

[Math.]  Two consecutive sums of consecutive numbers, (largest 11-digit): 21,538,881+…+21,543,522 = 21,543,523+…+21,548,163 = 99,994,257,363.

 

99,999,515,529

[Math.]  The largest 11-digit square number = 3162272.

 

99,999,900,000

[Math.]   (Sequence of numbers (10n–10m, n > 2m).

99,999,900,0002 = 9,999,980,000,010,000,000,000 = (99999800000+100000+00000)2.

 

99,999,990,000

[Math.]  (Sequence of numbers (10n–10m, n > 2m).

99,999,990,0002 = 9,999,998,000,000,100,000,000 = (99999980000+0010000+0000)2.

 

99,999,999,000

[Math.]  (Sequence of numbers (10n–10m, n > 2m).

99,999,999,0002 = 9,999,999,800,000,001,000,000 = (99999998000+000+01000+000)2.

 

99,999,999,625

[Math.]  (Sequence of numbers 9…9625)

99,999,999,6252 = 9,999,999,925,000,000,140,625.

 

99,999,999,900s (separate page)

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xy,zwv,abc,def

[Math.]  For any xy,zwv = 10,000 to 99,999, there are always six 6-digit numbers abc,edf such that xy,zwv +abc,def is equal to one of 6 digit-rotations of 142,857 and the number xy,zwv,abc,def is a multiple of 142,857.

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