All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Year Yearn 6 (Posted on 2023-12-11) Difficulty: 3 of 5
It is evident that: 2023= 7*172. Thus, 2023 is expressible in the form P*QR2.
Determine the three integers following 2023 having this property.
What are the three integers preceding 2023 that have this property?

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Computer Solution Comment 2 of 2 |
Of the 3 before and after, some can be formed in more than one way.
1936 [[1, 4, 4], [4, 2, 2]]
1944 [[6, 1, 8]]
2000 [[5, 2, 0]]
2023 [[7, 1, 7]]
2025 [[1, 4, 5], [9, 1, 5]]
2028 [[3, 2, 6]]
2048 [[2, 3, 2], [8, 1, 6]]

1936 = 1 * 44^2
1936 = 4 * 22^2
1944 = 6 * 18^2
2000 = 5 * 20^2
2023 = 7 * 17^2
2025 = 1 * 45^2
2025 = 9 * 15^2
2028 = 3 * 26^2
2048 = 2 * 32^2
2048 = 8 * 16^2

------------------
my_dict = {}
for a in range(1,10):
    for b in range(1,10):
        for c in range(10):
            x = a * (10*b + c)**2
            if x not in my_dict:
                my_dict[x] = [[a,b,c]]
            else:
                my_dict[x].append([a,b,c])

sort_my_dict = sorted(my_dict)

index_2023 = sort_my_dict.index(2023)

solutions = []
for i in range(index_2023 - 3, index_2023 + 4):
    print(sort_my_dict[i], my_dict[sort_my_dict[i]])
    solutions.append([sort_my_dict[i], my_dict[sort_my_dict[i]]])
print()
for s in solutions:
    for triplet in s[1]:
        print('{} = {} * {}{}^2'.format(s[0], triplet[0], triplet[1], triplet[2]))
print()
for key in my_dict:
    if len(my_dict[key]) >= 3:
        print(key, my_dict[key])

  Posted by Larry on 2023-12-11 09:02:36
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (9)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information