4,900

[Math.]  A pyramidal number (sum of all squares of integers from 1 to 24): 4900 = 12+22+…+232+242 = 702. The only pyramidal number that is a square. This is the only non-trivial solution of Watson’s equation: 12+22+…+x2 = y2.

(However, there are many formulas for solutions (n, x, y) of the equation: (n+1)2+(n+2)2+…+(n+x)2 = y2.  (References [10])

 

4,913

[Math.]  4913 = (4+9+1+3)3 = 173.

 

4,927

[Math.]  Two multiples of number 4927, 4927×4 = 19,708 and 4927×5 = 24,635, use each of 10 digits 0-9 once.

 

4,931

[Math.]  A prime number.

Two multiples of 4831, 4931×2 = 9862 and 4931×7 = 34,517, use each of 9 digits 1-9 once.

 

4,932

[Math.]  11,807,208 = 4932×2394 = 8631×1368.

 

4,944

[Math.]  22,218,336 = 4494×4944 = 2568´8652.

 

4,949

[Math.]  (Sequence of numbers 49…949…9).

49493 = 121,213,882,349 = (1212+1388+2349)3.

49492 = 24,492,601 and 24+4926–01 = 4949.  

 

4,950

[Math.]  A triangular number (sum of all integers from 1 to 99): 4950 = 1+2+…+98+99.

 

[Math.]  49504 = 600,372,506,250,000 = (600+3725+0625+0000)4.

 

[Math.]  (Sequence of numbers 49…950…0 and 50…050…0).

24,502,500 = (2450+2500)2 = 49502 and

25,502,500 = (2550+2500)2 = 50502 and 4950+5050 = 10000.

 

4,956

[Math.]  32,679,864 = 6594×4956 = 8673×3768.

 

4,959

[Math.]  The pair (4959, 4960) is called Smith brothers (consecutive Smith numbers).

 

4,997 & 4999

[Math.] 

94 = 47×2 and, reversely, 49 = 47+2

994 = 497×2 and, reversely, 499 = 497+2

9994 = 4997×2 and, reversely, 4999 = 4997+2

99994 = 49997×2 and, reversely, 49999 = 49997+2

...

4,999

[Math.]  A prime number.

Its odd powers end with 4,999. Its even powers end with 00001.