2,199,999,999,978 & 4,399,999,999,956 & 8,799,999,999,912

[Math.] 

(*)   8712 = 2178×4 & 8712×2178 = 18,974,736 = 4356²

8712…8712 = 2178…2178×4 & 8712…8712×2178…2178 = 4356…4356²

 

(**)   87912 = 21978×4 & 21978×87912 = 1,932,129,936 = 43956²

87912…87912 = 21978…21978×4 & 21978…21978×87912…87912 = 43956…43956²

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(***)   8,799,999,999,912 = 2,199,999,999,978×4 & 

2,199,999,999,978×8,799,999,999,912 = 4,399,999,999,956²

8799...9912…8799...9912 = 2199...9978…2199...9978×4 &

2199...9978…2199...9978×8799...9912…8799...9912 = 4399...9956…4399...9956²

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(****)   879…912 = 219…978×4 & 219…978×879…912 = 439…956²

879…912…879…912 = 219…978…219…978×4 &

219…978…219…978×879...912…879...912 = 439…956…439…956².

2,404,879,675,441

[Math.]  Euler numbers (or secant numbers) are defined by the infinite series: sec(x) = 1/cos(x) = 1+E₂(x²/2!)+E₄(x⁴/4!)+E₆(x⁶/6!)+…, where E₀ = 1, E₂ = –1, E₄ = 5, E₆ =  –61, E₈ = 1,385, E₁₀ = –50,521, E₁₂ = 2,702,765, E₁₄ = –199,360,981, E₁₆ = 19,391,512,145, E₁₈ = –2,404,879,675,441…

The odd-indexed Euler numbers are all 0.

The even-indexed Euler numbers have alternating signs.

 

2,999,999,999,996

[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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