perplexus.info :: Numbers : sod(N) = pod(sqrt(N))

sod(N) = pod(sqrt(N)) (Posted on 2023-02-09)

(a) Find two positive integers, N1 and N2, such that for each:
* the sum of digits of the integer equals the product of digits of its square root, and
* the digit '1' does not appear in either the original integer or its square root.

(b) Can you find any others?

(c) Can you explain why there would be so many more solutions if we allowed the digit '1' to appear?

No Solution Yet Submitted by Larry

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computer solution of (a) and (b) -- spoilers

| Comment 1 of 3

clc,clearvars

n=uint64(1:10000000);

sq=n.^2;

disp('starting')

for i=1:length(n)

tst=[char(string(n(i))) char(string(sq(i)))];

if isempty(strfind(tst,'1'));

if sod(sq(i))==pod(n(i))

disp([sq(i) n(i) sod(sq(i)) pod(n(i))])

end

where sod is

function sd = sod(n)

dgts=num2str(n) ;

sd=sum(dgts-48);

end

and pod is

function sd = pod(n)

dgts=num2str(n) ;

sd=prod(dgts-48);

end

(48 is the Ascii value of the zero character.)

finds only

     N        sqrt(N)    sod(N)   pod(sqrt(N))

    8649         93         27         27
27269284       5222         40         40

No others found up to 10,000,000 ^2,

Posted by Charlie on 2023-02-09 09:30:16

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