Determine the smallest fifth power having the first four digits (reading left to right) as 2,0,2,2.
What is the smallest number having this property?
Find A, the fifth root of 2022 and B, the fifth root of 2023.
Construct an Integer by appending left to right each digit A and B have in common
When you get to the first digit where they differ, append 1 more than A's digit.
Stop.
Repeat this process 4 more times for 2022*10^i and 2023*10^i, for i = 1,2,3,4
The integers this generates: [45831,7264,11513,18246,2892]
Take the smallest of the 5 Integers, raise it to the 5th power
202297931960159232 = 2892^5
---- computer check:
def isFifth(n):
""" Input an integer, Returns True iff it is a
perfect 5th power. """
if round(n**(.2))**5 == n:
return True
else:
return False
m = 2022
n = 2023
for i in range(5):
A = m*10**i
B = n*10**i
print(A, A**.2)
print(B, B**.2)
# from inspection of above printout
myIntegers = [45831,7264,11513,18246,2892]
print('\n',min(myIntegers)**5,'\n')
for i in range(5,100000):
i5 = i**5
if str(i5)[0:4] == '2022' :# and isFifth(i5):
print(i,i5)
Output:
2022 4.583067253218678
2023 4.58352048377078
20220 7.263672090217737
20230 7.264390412234379
202200 11.512144448055878
202300 11.513282911730048
2022000 18.245519366352763
2023000 18.247323709679822
20220000 28.917199436649906
20230000 28.920059128105823
202297931960159232
2892 202297931960159232
7264 20224564450583117824
11513 202275145998425128793
18246 2022266337290300858976
18247 2022820565070705516007
28918 20222799075907178121568
28919 20226295894109477760599
28920 20229793196015923200000
45831 202207223867161767338151
45832 202229284922789712658432
45833 202251347903886181844393
45834 202273412810577211979424
45835 202295479642988845646875
72637 2022038846751833892586957
72638 2022178038522053850803168
72639 2022317237957440953707199
72640 2022456445058311782400000
72641 2022595659824982926699201
72642 2022734882257770985139232
72643 2022874112356992564971443
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Posted by Larry
on 2023-04-30 12:53:48 |
P&P & calculator method
