benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Each positive integer a undergoes the following procedure in order to obtain the number d=d(a): (i) move the last digit of a to the first position to obtain the numb er b; (ii) squ…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Each positive integer aa undergoes the following procedure in order to obtain the number d=d(a)d = d\left(a\right): (i) move the last digit of aa to the first position to obtain the numb er bb; (ii) square bb to obtain the number cc; (iii) move the first digit of cc to the end to obtain the number dd. (All the numbers in the problem are considered to be represented in base 1010.) For example, for a=2003a=2003, we get b=3200b=3200, c=10240000c=10240000, and d=02400001=2400001=d(2003)d = 02400001 = 2400001 = d(2003).) Find all numbers aa for which d(a)=a2d\left( a\right) =a^2. [i]
Plain-text mathematical notation (without MathML)
Each positive integer a undergoes the following procedure in order to obtain the number d=d(a):

(i) move the last digit of a to the first position to obtain the numb er b;
(ii) square b to obtain the number c;
(iii) move the first digit of c to the end to obtain the number d.

(All the numbers in the problem are considered to be represented in base 10.)  For example, for a=2003, we get b=3200, c=10240000, and d=02400001=2400001=d(2003).)

Find all numbers a for which d(a)=a².

[i]
Original LaTeX notation
Each positive integer $a$ undergoes the following procedure in order to obtain the number $d = d\left(a\right)$:

(i) move the last digit of $a$ to the first position to obtain the numb er $b$;
(ii) square $b$ to obtain the number $c$;
(iii) move the first digit of $c$ to the end to obtain the number $d$.

(All the numbers in the problem are considered to be represented in base $10$.)  For example, for $a=2003$, we get $b=3200$, $c=10240000$, and $d = 02400001 = 2400001 = d(2003)$.)

Find all numbers $a$ for which $d\left( a\right) =a^2$.

[i]

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
6846ba48-9d16-5132-8392-c44be170047f
task_key
test--6846ba48-9d16-5132-8392-c44be170047f
task_revision_id
1
config / split
/ test

Official source

initial import