202 Jean-Marie De Koninck
232 + 412 + 1372 = 292 + 372 + 1372 = 312 + 972 + 1032 = 372 + 592 + 1272 =
372 + 972 + 1012 = 472 + 832 + 1092 = 592 + 832 + 1032 = 612 + 672 + 1132 =
672 + 712 + 1072 = 712 + 732 + 1032 = 732 + 792 + 972.
21 147
the ninth Bell number (see the number 52).
21 480
the
22nd
number n such that n! 1 is prime (see the number 166).
21 701
the exponent of the 25th Mersenne prime 221 701 1 (Noll and Nickel, 1978).
21 978
the fourth number (which is not a palindrome) which divides the number ob-
tained by reversing its digits (see the number 1 089).
22 020
the smallest number n such that n, n+1, n+2, n+3, n+4, n+5 are all divisible
by a square 1: here 22 020 =
22·3·5·367,
22 021 =
192·61,
22 022 =
2·7·112·13,
22 023 =
32
· 2447, 22 024 =
23
· 2753, 22 025 =
52
· 881 (see the number 242).
22 073
the second prime number q such that

p≤q
p is a perfect square: here

p≤22073
p = 25633969 =
50632:
the sequence of numbers satisfying this pro-
perty begins as follows: 23, 22 073, 67 187, 79 427, 10 729 219, . . .
22 434
the largest solution x of the diophantine equation
x2
+ 19 =
yn:
J.H.E. Cohn
[35] proved that the only three solutions of this equation, with n 2 and x 0,
are (x, y, n) = (9, 10, 2), (18,7,3) and (22 434,55,5).
22 440
one of the three numbers n such that the polynomial x5 −x±n can be factored;
the two others are n = 15 and n = 2 759 640: here x5 x ± 22 440 = (x2
12x + 55)(x3 ± 12x2 + 89x ± 408) (see S. Rabinowitz [166]).
Previous Page Next Page