# Problem Of The Week #505 August 8th 2022

• MHB
• anemone

#### anemone

Gold Member
MHB
POTW Director
Here is this week's POTW:

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If ##a,\,b,\,c## and ##d## are non-negative integers and ##a^2-b^2+cd^2=2022##, find the minimum value of ##a+b+c+d##.

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Thanks for the interesting problem. I guess
$$a=1,b=2,c=1,d=45;\ a+b+c+d=49$$
I would like to know the right answer.

anemone
Thanks for the interesting problem. I guess
$$a=1,b=2,c=1,d=45;\ a+b+c+d=49$$
I would like to know the right answer.
I am sorry. Your guess is incorrect.

I will wait a bit longer before posting the answer to this POTW, just in case there are others who would like to try it out.

The best I can do for now is:$$a = 17, b = 1, c = 6, d = 17; \ a + b + c + d = 41$$

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Well, I feel a bit guilty answering as it’s been an (extremely) long time since I was at school! However:
##a=0, b=1, c=7, d=17##
##a+b+c+d = 25##

anemone, bob012345, dextercioby and 1 other person
Opps! I didn't see @Steve4Physics 's answer above soon enough. Why can't I delete my wrong answer (27)?

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