The power of 5 must be:
1 less than a multiple of 5
a multiple of 42
The power of 6 must be
1 less than a multiple of 6
a multiple of 35
The power of 7 must be
1 less than a multiple of 7
a multiple of 30
To get these, the program:
for p5=42:42:999999
if mod(p5,5)==4
break
end
end
for p6=35:35:999999
if mod(p6,6)==5
break
end
end
for p7=30:30:999999
if mod(p7,7)==6
break
end
end
disp([p5,p6,p7])
disp([5^p5*6^p6*7^p7])
disp([sym(5)^p5*sym(6)^p6*sym(7)^p7])
shows the answer is
5^84 * 6^35 * 7^90
which is approximately the 163-digit number
1.01764834100024e+162
or exactly
1017648341000237270320329897336206925241596548387237973988224804540893494763882467
375145452669116252764069940894842147827148437500000000000000000000000000000000000
Verification:
>> a=sym(5)^p5*sym(6)^p6*sym(7)^p7
a =
1017648341000237270320329897336206925241596548387237973988224804540893494763882467
375145452669116252764069940894842147827148437500000000000000000000000000000000000
>> vpa(5*a)^(1/5)
ans =
347787161975600777636718750000000.0
>> vpa(6*a)^(1/6)
ans =
1351942320604862109375000000.0
>> vpa(7*a)^(1/7)
ans =
183937730694539062500000.0
>>
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Posted by Charlie
on 2024-10-28 08:28:13 |
solution
